AC_01_Basics_Multirate.ipynb

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        "<center>\n",
        "    <img src=\"https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/ac_header.png\">\n",
        "</center>\n",
        "\n",
        "### <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https://www.tu-ilmenau.de/mt-ams/personen/schuller-gerald/\">Prof. Dr. -Ing. Gerald Schuller</a> <br> <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https://www.tu-ilmenau.de/mt-ams/lehre/msp-and-adsp-tutorials/\">Jupyter Notebook: Renato Profeta</a>\n",
        "\n",
        "[Applied Media Systems Group](https://www.tu-ilmenau.de/en/applied-media-systems-group/) <br>\n",
        "[Technische Universität Ilmenau](https://www.tu-ilmenau.de/)"
      ]
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      "source": [
        "# Basics of Multirate Signal Processing\n",
        "\n",
        "## Lecture Video:\n",
        "\n",
        "https://youtu.be/Z28cSk93F6Y\n"
      ]
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        "Audio coders process sampled audio signals. As an input signal, they often have audio signals sampled at e.g. 48kHz or 44.1 kHz, and with 16 bits/sample.\n",
        "\n",
        "Internally they filter the signal and **down- and up-sample** it with **filter banks**, in the encoder and decoder. Hence before we take a closer look at the filter banks, we first take a short look at the basics of Multirate Signal Processing."
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      "source": [
        " - https://github.com/GuitarsAI/ADSP_Tutorials\n",
        " - https://github.com/GuitarsAI/MRSP_Notebooks"
      ]
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      "source": [
        "## Sampling, Downsampling, Upsampling, Sampling the Analog Signal, Normalized Frequency"
      ]
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        "To see what happens when we sample a signal, lets start with the analog signal s(t). Sampling it means to sample the signal at sample intervals *T*, or the sampling frequency $f_s$.\n",
        "\n",
        "Mathematically, sampling can be formulated as **multiplying** the analog signal with a **Dirac impulse** at the sampling time instances **nT**, where *n* is the number of our sample (n=0,… for causal systems).\n",
        "\n",
        "If we look at the Fourier transform of an analog time continuous system, we get:\n",
        "\n",
        "$$\\large\n",
        "S^c(\\omega) = \\int_{t=-\\infty}^{\\infty} S(t) \\cdot e^{-j\\omega t} dt\n",
        "$$\n",
        "\n",
        "where the superscript *c* denotes the continuous version, with $\\omega=2\\pi f.$\n",
        "\n",
        "If we now compute the Fourier transform for the sampled signal, we get a sum, because the Dirac impulse is not zero only at the sample time instances, and the integral over a Dirac impulse is one:\n",
        "\n",
        "$$\\large\n",
        "S^d(\\omega) = \\sum_{n=-\\infty}^{\\infty} S(nT) \\cdot e^{-j\\omega nT}\n",
        "$$\n",
        "\n",
        "with the superscript *d* now denoting the discrete time version.\n",
        "\n",
        "Now we can see that the frequency variable only appears as $\\omega nT$ , with *T* as the inverse of the sampling frequency. Hence we get:\n",
        "\n",
        "$$\\large\n",
        "\\omega T = \\dfrac{\\omega}{f_s}=:\\Omega\n",
        "$$\n",
        "\n",
        "This is now our normalized frequency, where $2\\pi$ represents the sampling frequency and $\\pi$ is the so-called *Nyquist frequency* (the upper limit of our usable frequency range).\n",
        "\n",
        "**Important Point:** We have a normalized frequency, normalized to the sampling frequency, where $2\\pi$ denotes the sampling frequency, and $\\pi$ is the *Nyquist frequency!* (since we have no time units in a sampled sequence).\n",
        "\n",
        "To indicate that we are now in the discrete domain, we rename our signal to x(n):=s(nT). Its spectrum or frequency response is then calculated with the **Discrete Time Fourier Transform:**\n",
        "\n",
        "$$\\large\n",
        "X(\\Omega) = \\sum_{n=-\\infty}^{\\infty} x(n) e^{-j\\Omega n}\n",
        "$$\n",
        "\n",
        "Because *n* in the exponent is integer here (no longer real valued like *t*), we get a $2\\pi$ periodicity for $X(\\Omega)$.\n",
        "\n",
        "This is the first important property for discrete time signals. The above transform is called the *Discrete Time Fourier* transform (not the Discrete Fourier Transform), which is for finite or periodic discrete time sequences. Here we still have an infinite \"block length\").\n",
        "\n",
        "Also observe that for real valued signals, the spectrum of the negative frequencies is the conjugate complex of the positive frequencies:\n",
        "\n",
        "$$\\large\n",
        "X(-\\Omega)=\\overline{X(\\Omega)}$$\n",
        "where $\\overline{X}$ denotes the conjugate complex operation, because in the sum of our DTFT we have:\n",
        "\n",
        "$$\\large\n",
        "e^{-j(-\\Omega)n}=e^{j\\Omega n} = e^{-j\\Omega n}$$"
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      "source": [
        "### Sampling a Discrete Time Signal"
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        "So what happens if we further downsample an already discrete signal x(n), to reduce its sampling rate?\n",
        "\n",
        "**Downsampling by N** means we only keep every Nth sample and discard every sample in between. Observe that this results in a **normalized frequency which is a factor of N higher**.\n",
        "\n",
        "This downsampling process can also be seen as first multiplying the signal with a sequence of **unit pulses** (a 1 at each sample position), zeros in between, and later dropping the zeros (just like with the Dirac impulses, but now with 1's instead of the Dirac impulses). This multiplication with the unit pulse train can now be used to mathematically analyse this downsampling, looking at the resulting spectra, first still including the zeros. The frequency response now becomes\n",
        "\n",
        "\n",
        "$$\\large X^d(\\Omega)=\\sum_{n=mN} x(n)e^{-j \\Omega n}$$\n",
        "$$\\large =\\sum_{m=- \\infty}^ \\infty x(mN)e^{-j \\Omega mN}$$\n",
        "for all integers m.\n",
        "\n",
        "Again we can write down-sampling as a multiplication of the signal with a sampling function. In continuous time it was the sequence of Dirac impulses, here it is a **sequence of unit pulses** at positions of multiples of N,\n",
        "\n",
        "$$\\large\n",
        "\\delta_N ( n ) = \\left ( \\matrix {{1 , \\text{if n = m N}} \\\\ {0 , \\text{else}}} \\right) $$\n",
        "\n",
        "Then the sampled signal, with the zeros still in it, becomes\n",
        "\n",
        "$$\\large\n",
        "x^d(n)=x(n)\\Delta _N (n)$$\n",
        "\n",
        "This signal is now an intermediate signal, which gets the zeros removed before transmission or storage, to reduce the needed data rate. The decoder upsamples it by re-inserting the zeros to obtain the original sampling rate.\n",
        "\n",
        "Observe that this is then also the signal  that we obtain after this upsampling in the decoder. Hence this signal looks interesting to us, because it appears in the encoder and also in the decoder."
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        "What does its spectrum or **frequency response** look like?\n",
        "\n",
        "We saw that the downsampled signal $x^d(n)$ can be written as the multiplication of the original signal with the unit pulse train $\\delta_N(n)$.\n",
        "\n",
        "In the spectrum or frequency domain this becomes a convolution with their Fourier transforms. The Fourier transform of the unit pulse train is a Dirac impulse train. But that is not so easy to derive, so we just apply a simple trick, to make it mathematically more easy and get converging sums. We have a guess what the Fourier transform of the unit pulse train is: we get Dirac impulses at frequencies of $\\large \\frac{2\\pi}{N}k.$\n",
        "\n",
        "Remember that the inverse Discrete Time Fourier transform is:\n",
        "\n",
        "$$\\large\n",
        "\\delta_N(n) = \\dfrac{1}{2\\pi} \\int_0^{2\\pi} \\Delta(\\Omega)e^{jn\\Omega}d\\Omega$$\n",
        "\n",
        "where\n",
        "$\\large\n",
        "\\Delta(\\Omega)=\\dfrac{2\\pi}{N}\\sum_{k=0}^{N-1}\\delta \\left(\\dfrac{2\\pi}{N}k \\right)$ is the Fourier transform of the unit pulse train.\n",
        "\n",
        "We can now apply the inverse Fourier transform to our guess, and use it in the time domain:\n",
        "\n",
        "$$\\large\n",
        "\\delta_N(n) = \\dfrac{1}{N} \\sum_{k=0}^{N-1}e^{j\\frac{2\\pi}{N}kn}\n",
        "$$\n",
        "\n",
        "Here we get $c=e^{j\\frac {2 \\pi}{N}n}$, and the sum can hence be computed in a closed form:\n",
        "\n",
        "$$ \\large\n",
        " \\sum _{k = 0}^{N - 1} {e^{j \\frac{2 π} { N} \\cdot n \\cdot k} } =\\frac{e^{j \\frac{2  π} { N} \\cdot n \\cdot N} - 1}  {e^{j \\frac{2  π} {N }\\cdot n} - 1}\n",
        "$$\n",
        "\n",
        "Now we have to prove that this is indeed true (since we only applied a guess). To do that, we can look at the sum. It is a geometric sum (a sum over a constant with the summation index in the exponent):\n",
        "\n",
        "$S= \\sum _{k = 0} ^ {N - 1} c^k$ , $S \\cdot c = \\sum _{k = 1} ^ N c^k$ , $S c -S =c^N -1$, hence we get:\n",
        "\n",
        "$$S =\\frac{c^N - 1}  {c - 1}$$\n",
        "\n",
        "In order to get our unit pulse train, this sum must become N for n=mN. We can check this by simply plugging this into the sum. The right part of the sum is undefined in this case (0/0), but we get an easy result by looking at the left hand side: $e^{j \\frac{2 π}{N} \\cdot m N \\cdot k} =1$. Hence the sum becomes N, as desired!<br>\n",
        "For $n  \\neq m N$ we need the sum to be zero. Here we can now use the right hand side of our equation. The denominator is unequal zero, and the numerator becomes zero, and hence the sum is indeed zero, as needed!\n",
        "\n",
        "This proves that our **assumption was right**. Now we can use this expression for the unit pulse train in the time domain and compute the Fourier transform,\n",
        "\n",
        "$$ \\large\n",
        "x^d \\left ( n \\right )  =x \\left ( n \\right )  \\cdot \\Delta_N \\left ( n \\right ) $$\n",
        "\n",
        "$$\\large\n",
        "=x  ( n  ) \\cdot \\frac{1}{N}  \\sum _ {k = 0} ^{N - 1} e^{j \\frac{2 π} {N} \\cdot k \\cdot n}\n",
        "$$\n",
        "\n",
        "Taking its Discrete Time Fourier transform now results in\n",
        "\n",
        "$$\\large\n",
        "X^d \\left ( \\Omega \\right )  = \\sum _ {n = - \\infty} ^ \\infty {x(n) \\cdot} \\frac{1}{ N}  \\sum _ {k = 0} ^{N - 1} e^{j \\frac{2\\pi}{ N}\\cdot k \\cdot n} \\cdot e^{- j\\Omega n} = $$\n",
        "\n",
        "$$\\large\n",
        "=\\frac{1} { N}  \\sum _ {k = 0}^ {N - 1}\\sum _{n=-\\infty}^{\\infty} {x  ( n )\\cdot e^{-j\\left(- \\frac{2\\pi}{N}\\cdot k +\\Omega\\right)\\cdot n}}$$\n",
        "\n",
        "$$\\large\n",
        "=\\frac{1} {N}  \\sum _{k = 0} ^{N - 1} {X  \\left(  - \\frac{2 \\pi}{ N} k + \\Omega  \\right)}\n",
        "$$\n",
        "\n",
        "We see, that sampling, still including the zeros, leads (in the frequency domain) to **multiple shifted versions of the signal spectrum**, the so-called **aliasing components** (N-1 aliasing components):\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "X^d (\\Omega)= \\frac{1} {N} \\sum _{k=0} ^{N-1} X \\left(- \\frac{2 \\pi}{N} \\cdot k + \\Omega\\right)\n",
        "\\end{equation}$$\n",
        "\n",
        "**In conclusion:** Sampling a signal by a factor of N, with keeping the zeros between the sample points, leads to N-1 aliasing components."
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        "**Example:**\n",
        "\n",
        "Make a sine wave which at 44100 Hz sampling rate has a frequency of 400 Hz at 1 second duration. Hence we need 44100 samples, and 400 periods of our sinusoid in this second. Hence we can write our signal in Python as:"
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        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "fs = 44100\n",
        "f = 400.0\n",
        "s=np.sin(2*np.pi*f*np.arange(0,1,1.0/fs))"
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type=\"audio/wav\" />\n",
              "                    Your browser does not support the audio element.\n",
              "                </audio>\n",
              "              "
            ],
            "text/plain": [
              "<IPython.lib.display.Audio object>"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import IPython.display as ipd\n",
        "ipd.Audio(s, rate=fs)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "t0IiuaP-NNk5",
        "outputId": "0b7ee988-9e57-46c3-fa4f-311be278f4c0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the first 1000 samples\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(s[0:1000])\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FS9YrXyGNNk5"
      },
      "source": [
        "Now we can multiply this sine tone signal with a unit pulse train, with N=8.\n",
        "We use an **indexing trick** to get the desired result of only keeping every 8th sample and having zeros in between:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ajyrUVtkNNk5",
        "outputId": "18579b22-81c2-468e-f20d-470f6586c51e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "sdu = np.zeros(44100)\n",
        "sdu[0::8]=s[0::8]\n",
        "\n",
        "# Now plot the result, the first 100 samples:\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(s[0:100], label='Original Signal')\n",
        "plt.stem(sdu[0:100],linefmt='r',markerfmt='r.', use_line_collection=True, label='Downsampled with zeros')\n",
        "plt.legend()\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q8YUcXTJNNk5"
      },
      "source": [
        "Now take a look at the spectrum of the original signal s:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ACsOYn3xNNk6",
        "outputId": "895f1fbe-a8be-4c3f-f8a0-780dd8b73e43"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "from scipy.signal import freqz\n",
        "w,H=freqz(s)\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(w, abs(H)+1e-3)\n",
        "plt.xlabel('Normalized Frequency: $\\pi$ is Nyquist freq.')\n",
        "plt.ylabel('Magnitude')\n",
        "plt.title('Spectrum of The Sinusoid')\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8UxWecrxNNk6"
      },
      "source": [
        "The plot shows the magnitude of the frequency spectrum of our signal. Observe that the frequency axis (horizontal) is a *normalized* frequency, normalized to the Nyquist frequency as $\\pi$, in our case 22050 Hz. Hence our sinusoid should appear as a peak at normalized frequency 400.0/22050*pi=0.05699, which we indeed see.\n",
        "\n",
        "Now we can compare this to our signal with the zeros, sdu:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "s8F6WvjaNNk6",
        "outputId": "d5f25124-734d-46ec-ff6e-e0c68b892314"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(10,8))\n",
        "w,H=freqz(s)\n",
        "plt.plot(w, abs(H))\n",
        "plt.xlabel('Normalized Frequency: $\\pi$ is Nyquist freq.')\n",
        "plt.ylabel('Magnitude')\n",
        "plt.title('Magnitude Spectrum of the Sinusoids')\n",
        "\n",
        "w,H=freqz(sdu)\n",
        "plt.plot(w, abs(H))\n",
        "plt.legend(('Original Sinusoid','Sampled Sinusoid with Zeros'))\n",
        "plt.grid();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kwPpPXToNNk6"
      },
      "source": [
        "Here we can see the original line of our 400 Hz tone, and now also the 7 new aliasing components. Observe that always 2 aliasing components are close together. This is because the original 400 Hz tone also has a spectral peak at the negative frequencies, at -400 Hz, or at normalized frequency -0.05699.\n",
        "\n",
        "Often, the small magnitude components on this plot are also interesting, for that reason magnitude frequency responses are usually plotted on a logarithmic Decibel (dB) scale, applying the function 20*log10(.) to it,"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "vpqm3cVJNNk6",
        "outputId": "7252a352-d021-4760-ce41-e7c00b84fbe7"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(10,8))\n",
        "w,H=freqz(sdu)\n",
        "plt.plot(w, 20*np.log10(abs(H)))\n",
        "plt.xlabel('Normalized Frequency: $\\pi$ is Nyquist freq.')\n",
        "plt.ylabel('Magnitude in dB')\n",
        "plt.title('Magnitude Spectrum of the  Downsampled Sinusoid in dB')\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WmU-wGBvNNk6"
      },
      "source": [
        "Observe that the small magnitudes become much more visible.\n",
        "\n",
        "Now also listen to the signal with the zeros:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hide_input": false,
        "id": "ZUvBT-0iNNk6",
        "outputId": "9ab809f5-9f97-4c83-9231-2838792b3f7b"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
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type=\"audio/wav\" />\n",
              "                    Your browser does not support the audio element.\n",
              "                </audio>\n",
              "              "
            ],
            "text/plain": [
              "<IPython.lib.display.Audio object>"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import IPython.display as ipd\n",
        "ipd.Audio(sdu, rate=44100)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XDuSPuvENNk6"
      },
      "source": [
        "Here you can hear that it sounds quite different from the original, because of the string of aliasing components!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0uCC80AKNNk6"
      },
      "source": [
        "### Real-Time Python Example\n",
        "\n",
        "*Note: Real-Time Audio Examples don't work inside cloud environments such as Google Colab and Binder.*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hide_input": true,
        "id": "Q2VGEM-mNNk6",
        "outputId": "b0b7ffd7-0cd2-4fb5-ab98-791b5a0e6c97"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/hbIQOeD4N2k?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/hbIQOeD4N2k?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SCaZfKguNNk6"
      },
      "source": [
        "**Python** real time audio **example**: This example takes the microphone input and samples it, without removing the zeros, and plays it back the the speaker in real time.\n",
        "\n",
        "It constructs a unit pulse train, with a 1 at every N'th sample, using the modulus function „%“,\n",
        "\n",
        "```s=(np.arange(0,CHUNK)%N)==0```\n",
        "\n",
        "Here you can hear the microphone signal as it is sampled at 32 kHz sampling rate, and then multiplied with a unit pulse train, and then played out, again at 32 kHz sampling rate.\n",
        "\n",
        "Observe: you can hear the high frequency aliasing artifacts, which sound a little like ringing. You can play with the script and see how the sound changes when you change the downsampling rate \"N\" in the script."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8xfFBTIyNNk6",
        "outputId": "4ed19118-7ce0-4e80-bd27-74b892a78ad4",
        "colab": {
          "referenced_widgets": [
            "2d0ad360d986443f872b40f981f676c1",
            "5215a83d08cb4454827ae35947999072"
          ]
        }
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "2d0ad360d986443f872b40f981f676c1",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "ToggleButton(value=False, description='Stop')"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "5215a83d08cb4454827ae35947999072",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Checkbox(value=False, description='Downsampling with Zeros')"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "PyAudio terminated...\n"
          ]
        }
      ],
      "source": [
        "\"\"\"\n",
        "PyAudio Example: Make a sampling between input and output\n",
        "(i.e., record a few samples, multiply them with a unit pulse train,\n",
        "and play them back immediately).\n",
        "Using block-wise processing instead of a for loop\n",
        "Gerald Schuller, Octtober 2014\n",
        "\n",
        "Updated and Ported to Jupyter Notebooks by: Renato Profeta, November 2019\n",
        "\"\"\"\n",
        "\n",
        "import time\n",
        "import numpy as np\n",
        "from pyaudio import PyAudio, paFloat32, paContinue, paInt16, paComplete\n",
        "from ipywidgets import ToggleButton, Checkbox\n",
        "import threading\n",
        "\n",
        "sampling_on=False\n",
        "\n",
        "button_stop= ToggleButton(description='Stop')\n",
        "box_sampling = Checkbox(False, description='Downsampling with Zeros')\n",
        "\n",
        "def on_button_stop(change):\n",
        "    if change['new']==True:\n",
        "        stream.stop_stream()\n",
        "        stream.close()\n",
        "        pa.terminate()\n",
        "        button_stop.disabled=True\n",
        "        print('PyAudio terminated...')\n",
        "button_stop.observe(on_button_stop, 'value')\n",
        "display(button_stop)\n",
        "\n",
        "def box_sampling_changed(box_sampling):\n",
        "    global SamplingOn\n",
        "    if box_sampling['new']:\n",
        "        SamplingOn=True\n",
        "    else:\n",
        "        SamplingOn=False\n",
        "box_sampling.observe(box_sampling_changed, names='value')\n",
        "display(box_sampling)\n",
        "\n",
        "N=8\n",
        "s=(np.arange(0,1024)%N)==0\n",
        "SamplingOn=False\n",
        "\n",
        "\n",
        "def callback(in_data, frame_count, time_info, flag):\n",
        "    global SamplingOn\n",
        "    audio_data = np.frombuffer(in_data, dtype=np.int16)\n",
        "    audio_data_s = audio_data\n",
        "    if SamplingOn:\n",
        "        audio_data_s=audio_data*s\n",
        "    if button_stop.value==True:\n",
        "        return (audio_data_s, paComplete)\n",
        "    return (audio_data_s, paContinue)\n",
        "\n",
        "pa = PyAudio()\n",
        "\n",
        "stream = pa.open(format = paInt16,\n",
        "                 channels = 1,\n",
        "                 rate = 32000,\n",
        "                 output = True,\n",
        "                 input = True,\n",
        "                 frames_per_buffer = 1024,\n",
        "                 stream_callback = callback)\n",
        "\n",
        "\n",
        "def keep_alive(button_stop):\n",
        "    while stream.is_active():\n",
        "        if button_stop.value==True:\n",
        "            break\n",
        "        time.sleep(0.1)\n",
        "\n",
        "# Create a Thread for run_spectrogram function\n",
        "thread = threading.Thread(target=keep_alive, args=(button_stop,))\n",
        "stream.start_stream()\n",
        "thread.start()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VBA7kCG6NNk6"
      },
      "source": [
        "## Removing the Zeros"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hide_input": true,
        "id": "entSw765NNk6",
        "outputId": "2e166995-6623-4a5f-c20a-c6be040d13a2"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/XGKfAm1-Mek?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/XGKfAm1-Mek?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b8xfoVySNNk6"
      },
      "source": [
        "The final step of downsampling is now to omit the zeros between the samples, to obtain the lower sampling rate. Let's call the signal without the zeros  $y(m)$ where the time index m denotes the **lower sampling rate** (as opposed to n, which denotes the higher sampling rate).\n",
        "\n",
        "In our Python example this is:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sqAMTx5eNNk6",
        "outputId": "0e8cc8cb-9ec5-4dfb-c5ab-6e2fb48cac00"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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Y8isU4LXXiB07oLOzuC5J0jBgEFN+TU0wYgQJYPTo4rokScOAQUz5NTbC1KlsOeooaG4urkuSNAzU5C5AAmDcOLamxFhDmCRpGBmQGbGImBERT0bEmoiY38f+6yOitfTxWER0RcQbS/vWR8Sq0r7lA1GPpCGqpQU++1nf0CFpyCh7RiwiRgK3ABcCbcCyiFiSUnp85zEppRuBG0vH/yFwXUrp1z2e5oKU0svl1iJpCCu9u5bOzuJrCb2MLWkIGIgZsQZgTUppbUqpE7gLmLWX4y8D7hyAcSUNJ6V319LV5btrJQ0ZAxHEjgF+2WO9rbRtNxHxOmAG8J0emxPw/YhYERFzB6AeSUNR6d21gO+ulTRkDMSL9aOPbWkPx/4h8Eivy5LnppSei4gJwAMR8fOU0oO7DVIMaXMBamtrKQzy/4Y7OjoGfQz9Vl17O11dXVXX87r2dgBaq7Duauz3mccfT01HB098/OO8snVrVc2K+TOlsux3ZdnvAzcQQawNOLbH+kTguT0cO5telyVTSs+VHl+MiHspXurcLYillBYCCwHq6+tT0yD/b7hQKDDYY6iH8eNpb2+vvp6PHw9QlXVXZb+PKU62n3H11ZkL2X/+TKks+11Z9vvADcSlyWXACRExOSJGUwxbS3ofFBHjgLcD9/XYdmhEHLZzGbgIeGwAapIkSTrolT0jllLaHhHzgPuBkcCilNLqiLiqtH9B6dD3AN9PKf2mx+m1wL0RsbOWb6WU/rPcmiRJkqrBgNzQNaW0FFjaa9uCXuvfAL7Ra9ta4PSBqEGSJKna+CeOJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyGZAgFhEzIuLJiFgTEfP72N8UEZsiorX08cn+nitJkjRU1ZT7BBExErgFuBBoA5ZFxJKU0uO9Dn0opfTOAzxXkiRpyBmIGbEGYE1KaW1KqRO4C5hVgXMlSZKq2kAEsWOAX/ZYbytt660xIn4WEf8REafu57mSJElDTtmXJoHoY1vqtf4T4LiUUkdEzAT+DTihn+cWB4mYC8wFqK2tpVAoHGi9/dLR0THoY+i36trb6erqqrqe17W3A9BahXXb78ryZ0pl2e/Kst8HbiCCWBtwbI/1icBzPQ9IKb3SY3lpRHw1Io7sz7k9zlsILASor69PTU1NA1D6nhUKBQZ7DPUwfjzt7e3V1/Px4wGqsm77XVn+TKks+11Z9vvADcSlyWXACRExOSJGA7OBJT0PiIijIiJKyw2lcTf251xJkqShquwZsZTS9oiYB9wPjAQWpZRWR8RVpf0LgPcCfxYR24HXgNkppQT0eW65NUmSJFWDgbg0SUppKbC017YFPZa/Anylv+dKkiQNB95ZX5IkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiA0lLS3w2c8WHyVJ0kFvQG5foYNASwtMnw6dnTB6NDQ3Q2Nj7qokSdJeOCM2VBQK8Npr0NVVDGP+zS9Jkg56BrGhoqkJRpS+nKNHF9clSdJBzSA2VDQ2wtSpMHmylyUlSaoSvkZsKBk3rvhhCJMkqSo4IyZJkpSJQUySJCkTg5gkSVImBjFJGmwtLbx58WJvtixpNwYxSRpMpZstT160qHjTZcOYpB4MYpI0mEo3W44dO7zZsqTdGMQkaTCVbracwJstS9qNQUySBlPpZstbjjrKmy1L2o03dJWkwTZuHFtTYqwhTFIvzohJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMBiSIRcSMiHgyItZExPw+9r8/IlaWPn4UEaf32Lc+IlZFRGtELB+IeiRJkqpBTblPEBEjgVuAC4E2YFlELEkpPd7jsHXA21NK/xMRlwALgbN77L8gpfRyubVIkiRVk4GYEWsA1qSU1qaUOoG7gFk9D0gp/Sil9D+l1R8DEwdgXEmSpKpW9owYcAzwyx7rbew629Xbh4D/6LGegO9HRAJuSykt7OukiJgLzAWora2lUCiUU/M+dXR0DPoYA62uvR2A1iqrG4q1d3V12fMKsd+VVa39rmbV+DO8mtnvAzcQQSz62Jb6PDDiAopB7Pd6bD43pfRcREwAHoiIn6eUHtztCYsBbSFAfX19ampqKrvwvSkUCgz2GANu/HiA6qsbYPx42tvbq6/2au25/a6sau13FavKn+FVzH4fuIG4NNkGHNtjfSLwXO+DImIq8HVgVkpp487tKaXnSo8vAvdSvNQpSZI05A1EEFsGnBARkyNiNDAbWNLzgIh4M3APcEVK6ake2w+NiMN2LgMXAY8NQE2SJEkHvbIvTaaUtkfEPOB+YCSwKKW0OiKuKu1fAHwSOAL4akQAbE8p1QO1wL2lbTXAt1JK/1luTZIkSdVgIF4jRkppKbC017YFPZY/DHy4j/PWAqf33i5JkjQceGd9SZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMBiSIRcSMiHgyItZExPw+9kdEfKm0f2VEnNHfcyVJkoaqsoNYRIwEbgEuAU4BLouIU3oddglwQuljLnDrfpxbeS0tvHnxYmhpyV2JJEkawmoG4DkagDUppbUAEXEXMAt4vMcxs4BvppQS8OOIGB8RRwOT+nFuZbW08Pyl72VETQ2/eOAHcPrpcPjh2crZLxt/XXy84o/z1nEgNv6a7du3s6naaq/WntvvyqrWflexN7S384vbF+UuY9io5n4fcvJJHPXRj2YbfyCC2DHAL3ustwFn9+OYY/p5LgARMZfibBq1tbUUCoWyit6TNy9ezOu6uoiaGtKOHWx5fgNbd+wYlLEG3KRJxcf29pxVHJhJk+jq6mJktdVerT2335VVpf1+/Zo1AHS85S2ZK9k/r1+zhkNJtL/lhNyl7Bf7XXmvX7MGfvITCueck62GgQhi0ce21M9j+nNucWNKC4GFAPX19ampqWk/StwPhxwCixez4+WtjDjkELj7LmhsHJyxtItCocCgfV21G/tdWVXZ7531/vuSrGXst6Ym2tvbeUsV1g3Y70oq9fy4jP82B+LF+m3AsT3WJwLP9fOY/pxbWY2N0NzM+iuvhOZmQ5gkSRo0AzEjtgw4ISImA78CZgOX9zpmCTCv9Bqws4FNKaUNEfFSP86tvMZGnt26leMNYZIkaRCVHcRSStsjYh5wPzASWJRSWh0RV5X2LwCWAjOBNcCrwAf3dm65NUmSJFWDgZgRI6W0lGLY6rltQY/lBFzd33MlSZKGA++sL0mSlIlBTJIkKRODmCSpb5s2wbPP+ldGpEFkEJMk7a6lBVauhHXrYPp0w5g0SAxikqTdFQoQpXtud3YW1yUNOIOYJGl3TU0wejSMHFl8rLa/CiBViQG5fYUkaYgp/ZURCoViCPMG19KgMIhJkvrW2GgAkwaZlyYlSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMikriEXEGyPigYh4uvT4hj6OOTYifhgRT0TE6oi4pse+T0XEryKitfQxs5x6JEmSqkm5M2LzgeaU0glAc2m9t+3AX6WUTgbeBlwdEaf02P+FlFJd6WNpmfVIkiRVjXKD2CzgjtLyHcC7ex+QUtqQUvpJaXkz8ARwTJnjSpIkVb1yg1htSmkDFAMXMGFvB0fEJGAa8N89Ns+LiJURsaivS5uSJElDVc2+DoiIHwBH9bHrY/szUES8HvgOcG1K6ZXS5luBvwdS6fEfgSv3cP5cYC5AbW0thUJhf4bfbx0dHYM+hnZlzyvLfleW/a6cuvZ2urq6qq7fde3tALRWYd3V2G84OHoeKaUDPzniSaAppbQhIo4GCimlE/s4bhTwXeD+lNLNe3iuScB3U0qn7Wvc+vr6tHz58gOuuz8KhQJNTU2DOoZ2Zc8ry35Xlv2uoKYm2tvbGd/amruS/bPz+6PaAk219hsq1vOIWJFSqu9rX7mXJpcAc0rLc4D7+hg8gNuBJ3qHsFJ42+k9wGNl1iNJklQ1yg1inwMujIingQtL60TEmyJi5zsgzwWuAH6/j9tUfD4iVkXESuAC4Loy65EkSaoa+3yN2N6klDYC0/vY/hwws7T8MBB7OP+KcsaXJEmqZt5ZX5IkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkjS0bNrEIS+8AC0tuSuR9qmsIBYRb4yIByLi6dLjG/Zw3PqIWBURrRGxfH/PlySpX1paYOVKxjz/PEyfbhjTQa/cGbH5QHNK6QSgubS+JxeklOpSSvUHeL4kSXtXKEAEAdDZWVyXDmLlBrFZwB2l5TuAd1f4fEmSfqupCUaPZseIETB6dHFdOoiVG8RqU0obAEqPE/ZwXAK+HxErImLuAZwvSdK+NTZCczPrr7wSmpuL69JBrGZfB0TED4Cj+tj1sf0Y59yU0nMRMQF4ICJ+nlJ6cD/OpxTg5gLU1tZSGOTp5o6OjkEfQ7uy55VlvyvLfldWx6xZPLt1a1VdmqxrbwegtYpqhmLdXV1dVfn9fTD0fJ9BLKX0jj3ti4gXIuLolNKGiDgaeHEPz/Fc6fHFiLgXaAAeBPp1funchcBCgPr6+tQ0yNPNhUKBwR5Du7LnlWW/K8t+V1ZV9nv8eICqrLu9vb366oaDouflXppcAswpLc8B7ut9QEQcGhGH7VwGLgIe6+/5kiRJQ1W5QexzwIUR8TRwYWmdiHhTRCwtHVMLPBwRPwMeBb6XUvrPvZ0vSZI0HOzz0uTepJQ2AtP72P4cMLO0vBY4fX/OlyRJGg68s74kSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZIkZWIQkyRJysQgJkmSlIlBTJIkKRODmCRJUiZlBbGIeGNEPBART5ce39DHMSdGRGuPj1ci4trSvk9FxK967JtZTj2SJEnVpNwZsflAc0rpBKC5tL6LlNKTKaW6lFIdcCbwKnBvj0O+sHN/SmlpmfVIkiRVjXKD2CzgjtLyHcC793H8dOCZlNIvyhxXkiSp6pUbxGpTShsASo8T9nH8bODOXtvmRcTKiFjU16VNSZKkoapmXwdExA+Ao/rY9bH9GSgiRgPvAv62x+Zbgb8HUunxH4Er93D+XGAuQG1tLYVCYX+G328dHR2DPoZ2Zc8ry35Xlv2urGrsd117OwCtVVh3V1dX1fUbDo6e7zOIpZTesad9EfFCRBydUtoQEUcDL+7lqS4BfpJSeqHHc3cvR8TXgO/upY6FwEKA+vr61NTUtK/Sy1IoFBjsMbQre15Z9ruy7HdlVWW/x48HqMq629vbq69uOCh6Xu6lySXAnNLyHOC+vRx7Gb0uS5bC207vAR4rsx5JkqSqUW4Q+xxwYUQ8DVxYWici3hQR3e+AjIjXlfbf0+v8z0fEqohYCVwAXFdmPZIkSVVjn5cm9yaltJHiOyF7b38OmNlj/VXgiD6Ou6Kc8SVJkqqZd9aXJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZJ0MNi0CZ59FlpacleiCjKISZKUW0sLrFwJ69bB9OmGsWHEICZJUm6FAkQUlzs7i+saFgxikiTl1tQEo0fDyJHFx6am3BWpQsr6W5OSJGkANDZCc3NxJqypqbiuYcEgJknSwaCx0QA2DHlpUpIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUiUFMkiQpE4OYJElSJgYxSZKkTAxikiRJmRjEJEmSMjGISZKk4WnTJnj2WWhpyVaCQUySJA0/LS2wciWsWwfTp2cLYwYxSZI0/BQKEFFc7uwsrmdgEJMkScNPUxOMHg0jRxYfm5qylFGTZVRJkqScGhuhubk4E9bUVFzPwCAmSZKGp8bGbAFsJy9NSpIkZWIQkyRJB27TJg554YWst4CoZmUFsYh4X0SsjogdEVG/l+NmRMSTEbEmIub32P7GiHggIp4uPb6hnHokSVIFlW4BMeb557PeAqKalTsj9hjwv4AH93RARIwEbgEuAU4BLouIU0q75wPNKaUTgObSuiRJqgalW0AEZL0FRDUrK4illJ5IKT25j8MagDUppbUppU7gLmBWad8s4I7S8h3Au8upR5IkVVDpFhA7RozIeguIalaJd00eA/yyx3obcHZpuTaltAEgpbQhIibs6UkiYi4wF6C2tpbCIKfujo6OQR9Du7LnlWW/K8t+V5b9rpzDb7yRsY8+ymsNDbyydauzYvtpn0EsIn4AHNXHro+llO7rxxjRx7bUj/N2PSGlhcBCgPr6+tQ0yKm7UCgw2GNoV/a8sux3ZdnvyrLfFdTUROHUU+33AdpnEEspvaPMMdqAY3usTwSeKy2/EBFHl2bDjgZeLHMsSZKkqlGJ21csA06IiMkRMRqYDSwp7VsCzCktzwH6M8MmSZI0JJR7+4r3REQb0Ah8LyLuL21/U0QsBUgpbQfmAfcDTwDfTimtLj3F54ALI+Jp4MLSuiRJ0rBQ1ov1U0r3Avf2sf05YGaP9aXA0j6O2whML6cGSZKkauWd9SVJkjIxiEmSJGViEJMkScrEICZJkpSJQUySJCkTg5gkSVImBjFJkqRMDGKSJEmZGMQkSZIyMYhJkiRlYhCTJEnKxCAmSZKUSaSUctew3yLiJeAXgzzMkcDLgzyGdmXPK8t+V5b9riz7XVn2e++OSyn9Tl87qjKIVUJELE8p1eeuYzix55VlvyvLfleW/a4s+33gvDQpSZKUiUFMkiQpE4PYni3MXcAwZM8ry35Xlv2uLPtdWfb7APkaMUmSpEycEZMkScrEINaHiJgREU9GxJqImJ+7nqEsIo6NiB9GxBMRsToirsld03AQESMj4qcR8d3ctQwHETE+Iv41In5e+l5vzF3TUBYR15V+njwWEXdGxJjcNQ0lEbEoIl6MiMd6bHtjRDwQEU+XHt+Qs8ZqYhDrJSJGArcAlwCnAJdFxCl5qxrStgN/lVI6GXgbcLX9rohrgCdyFzGM/F/gP1NKJwGnY+8HTUQcA/wlUJ9SOg0YCczOW9WQ8w1gRq9t84HmlNIJQHNpXf1gENtdA7AmpbQ2pdQJ3AXMylzTkJVS2pBS+klpeTPFX1DH5K1qaIuIicAfAF/PXctwEBGHA+cDtwOklDpTSu1Zixr6aoCxEVEDvA54LnM9Q0pK6UHg1702zwLuKC3fAby7kjVVM4PY7o4BftljvQ2DQUVExCRgGvDfmUsZ6r4I/A2wI3Mdw8XxwEvAP5UuB389Ig7NXdRQlVL6FXAT8CywAdiUUvp+3qqGhdqU0gYo/gcbmJC5nqphENtd9LHNt5YOsoh4PfAd4NqU0iu56xmqIuKdwIsppRW5axlGaoAzgFtTStOA3+Blm0FTem3SLGAy8Cbg0Ij4QN6qpD0ziO2uDTi2x/pEnNYeVBEximIIW5xSuid3PUPcucC7ImI9xcvuvx8R/y9vSUNeG9CWUto50/uvFIOZBsc7gHUppZdSStuAe4BzMtc0HLwQEUcDlB5fzFxP1TCI7W4ZcEJETI6I0RRf5Lkkc01DVkQExdfOPJFSujl3PUNdSulvU0oTU0qTKH5v/1dKydmCQZRSeh74ZUScWNo0HXg8Y0lD3bPA2yLidaWfL9PxzRGVsASYU1qeA9yXsZaqUpO7gINNSml7RMwD7qf4bptFKaXVmcsays4FrgBWRURradtHU0pL85UkDbi/ABaX/nO3Fvhg5nqGrJTSf0fEvwI/ofiu7J/iXd8HVETcCTQBR0ZEG/B/gM8B346ID1EMw+/LV2F18c76kiRJmXhpUpIkKRODmCRJUiYGMUmSpEwMYpIkSZkYxCRJkjIxiEmSJGViEJMkScrEICZJkpTJ/wc/LFbvcYtFpwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "sd = sdu[0:44100:8]\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.stem(sd[0:int(100/8)],linefmt='r',markerfmt='r.', use_line_collection=True, label='Downsampled without zeros')\n",
        "plt.legend()\n",
        "plt.grid();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yL_Ktik5NNk6"
      },
      "source": [
        "Observe that here we only have $\\frac{100}{8}\\approx 12$ samples left."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rCYYuArWNNk6"
      },
      "source": [
        "How are the frequency responses or spectra of $y(m)$ and $x^d(n)$ connected?\n",
        "\n",
        "We can simply take the Fourier transforms of them,\n",
        "\n",
        "$$ \\large\n",
        "X^d (\\Omega)=\\sum _ {n=- \\infty}^ \\infty x^d (n) \\cdot  e^{-j \\Omega n}\n",
        "$$\n",
        "\n",
        "still with the zeros in it. Hence most of the sum contains only zeros. Now we only need to let the sum run over the non-zeros entries (only every Nth entry), by replacing n by mN, and we get\n",
        "\n",
        "$$ \\large\n",
        "X^d (\\Omega)=\\sum _ {n=mN} x^d (n) \\cdot  e^{-j \\Omega n}\n",
        "$$\n",
        "\n",
        "for all integer m, now without the zeros. Now we can make the connection to the Fourier transform of y(m), by making the index substitution m for n in the sum,\n",
        "\n",
        "\n",
        "$$ \\large\n",
        "X^d (\\Omega)= \\sum _{m=- \\infty} ^ \\infty y(m) \\cdot  e^{-j \\Omega \\cdot N m} = Y(\\Omega \\cdot N)\n",
        "$$\n",
        "\n",
        "This is now our result. It shows that the downsampled version (with the removal of the zeros), has the same frequency response, but the frequency variable $\\Omega$ is scaled by the factor N.\n",
        "\n",
        "For instance, the normalized frequency $\\pi /N$ before downsampling becomes $\\pi$ after removing the zeros! It shows that a **small part of the spectrum before downsampling becomes the full usable spectrum after downsampling.**\n",
        "\n",
        "Observe that we don't loose any frequencies this way, because by looking at eq. (1) we see that we obtain multiple copies of the spectrum in steps of $2\\pi /N$, and hence the spectrum already has a periodicity of $2\\pi /N$. This means that the spectrum between $-\\pi/N$ and $\\pi/N$ for instance (we could take any period of length $2\\pi /N$) contains a unique and full part of the spectrum, because the rest is just a periodic continuation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pDKXmD0wNNk6"
      },
      "source": [
        "We can now take a look at the spectrum with :"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QKIa0ggsNNk9"
      },
      "source": [
        "Observe that the sine signal now appear at normalized frequency of 0.455, a **factor of 8 higher** than before, with the zeros in it, because we **reduced the sampling rate by 8**.\n",
        "\n",
        "This is because we now have a new Nyquist frequency of 22050/8 now, hence our normalized frequency becomes $400*3.14 / 22050.8 \\approx 0.455$. This means removing the zeros scales or stretches our frequency axis.\n",
        "\n",
        "    \n",
        "Observe that in our time-domain plot, we only have $100/8 \\approx12$ samples left."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "suNoXccNNNk9"
      },
      "source": [
        "This can be seen in following pictures,\n",
        "<center>\n",
        "<img src='https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/Lecture6-6.png' width='700'>\n",
        "</center>\n",
        "\n",
        "Figure: The magnitude spectrum of a signal. The 2 boxes symbolize the passband of an ideal bandpass, here a high pass.\n",
        "\n",
        "<img src='https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/Lecture6-8.png' width='700'>\n",
        "Figure: The signal spectrum after passing through the high pass.\n",
        "\n",
        "<img src='https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/Lecture6-7.png' width='700' >\n",
        "\n",
        "Figure: Signal spectrum after multiplication with the unit pulse train, for N=2, hence setting every second value to zero (the zeros still in the sequence). Observe that we shift and add the signal by multiples of $2\\pi /2=\\pi$, and in effect we obtain „mirrored“ images of the high frequencies to the low frequencies (since we assume a real valued signal). Observe that the mirrored spectra and the original spectrum don't overlap, which makes reconstruction easy.\n",
        "\n",
        "<img src='https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/Lecture6-9.png' width='700'>\n",
        "\n",
        "Figure: Signal spectrum after downsampling (removing the zeros) by N (2 in this example). Observe the stretching of the spectrum by a factor of 2.\n",
        "\n",
        "**In conclusion:** Removing the N-1 zeros between samples stretches the spectrum of the signal by a factor of N."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YQK28yznNNk9"
      },
      "source": [
        "## Upsampling"
      ]
    },
    {
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              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/bIYXoAUISNs?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
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        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/Ow_FOJS82gc?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/bIYXoAUISNs?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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        "id": "GncvTxx8NNk9"
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      "source": [
        "What is still missing in our system is the upsampling, as the opposite operation of downsampling, for the case where we would like to increase our sampling rate. One of the first (**wrong!**) approaches to upsampling that often comes to mind if we want to do upsampling by a factor of N, is to simply repeat every sample N-1 times.\n",
        "\n",
        "**But** this is equivalent to first inserting N-1 zeros after each sample, and then filter the resulting sequence by a **low pass** filter with an impulse response of N ones. This is a very special case, and we would like to have a more general case.\n",
        "\n",
        "In our case, we actually a high pass filter, not a low pass. Hence we assume that we upsample by always first inserting N-1 **zeros** after each sample, and then have some interpolation filter for it (can also be a **high or band pass**, as needed to reconstruct a signal).\n",
        "\n",
        "Again we take the signal at the lower sampling rate as $y(m)$, with index m for the lower sampling rate, and the signal at the higher sampling rate, with the zeros in it, as $x^d(n)$ with index n for the higher sampling rate. Here we can see that this is simply the reverse operation of the final step of removing the zeros for the downsampling.\n",
        "\n",
        "Hence we can take our result from downsampling and apply it here:\n",
        "\n",
        "$$X^d(\\Omega)=Y(\\Omega \\cdot N)$$\n",
        "$$or$$\n",
        "$$X^d(\\Omega /N)=Y(\\Omega )$$\n",
        "\n",
        "We are now just coming from y(m), going to the now upsampled signal $x^d(n)$.\n",
        "\n",
        "For instance if we had the frequency $\\pi$ before upsampling, it becomes $\\pi /2$ for the upsampled signal, if we have N=2. In this way we now get an „extended“ frequency range.\n",
        "\n",
        "Since the spectrum before upsampling was also $2\\pi$ periodic, the extra spectrum we obtain contains a periodic continuation of our spectrum, which again is aliasing, which we would like to supress using filters (lowpass or bandpass) after upsampling."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "87DtPT6-NNk9"
      },
      "source": [
        "We saw the effects of downsampling and upsampling. Observe that we can perfectly reconstruct the high pass signal in our example if we use ideal filters, using upsampling and ideal high pass filtering.\n",
        "\n",
        "In this way we have for the analysis and synthesis the following picture:\n",
        "\n",
        "<center>\n",
        "    <br>\n",
        "    <img src='https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/lecture6-10.png' width='700'>\n",
        "</center>\n",
        "\n",
        "Observe that we **violate the conventional Nyquist** criterium, because our high pass passes the high frequencies. But then the sampling **mirrors** those frequencies **to the lower range**, such that we can apply the traditional Nyquist sampling theorem. This method is also known as bandpass Nyquist. This is an important principle for filter banks and wavelets. It says that we can perfectly reconstruct a bandpass signal in a filter bank, if we sample with twice the rate as the **bandwidth** of our bandpass signal (assuming ideal filters, to avoid spectral overlap of aliasing components)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3ARR0321NNk9"
      },
      "source": [
        "## Effects in the z-Domain"
      ]
    },
    {
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      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/e1xQJDLMHHE?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ]
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        "id": "V74dp8BrNNk9"
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      "source": [
        "The z-Transform is a more general transform than the Fourier transform, and we will use it to obtain perfect reconstruction in filter banks and wavelets. Hence we will now look at the effects of sampling and some more tools in the z-domain.\n",
        "\n",
        "Since we usually deal with causal systems in practice, we use the 1-sided z-Transform, defined as\n",
        "\n",
        "$$\\large\n",
        "X(z)=\\sum _{n=0} ^ {\\infty} x(n)z^{-n}\n",
        "$$\n",
        "\n",
        "Observe that a multiplication of the z-transform with $z^{−1}$ can be interpreted as a delay of the signal by 1 sample. It can be implemented as a delay or memory element.\n",
        "\n",
        "First observe that we get our usual frequency response (the Discrete Time Fourier Transform) if we evaluate the z-tranform along the unit circle in the z-domain,\n",
        "\n",
        "$$\\large\n",
        "z=e^{j\\Omega}\n",
        "$$\n",
        "\n",
        "What is now the effect of **multiplying our signal with the unitpulse** train in the z-domain? To see this we simply apply the z-transform, and use our sum formulation for the delta impulse train,\n",
        "\n",
        "$$\\large\n",
        "X^d(z)=\\sum_{n=0} ^ {\\infty} x(n) \\Delta_N(n) z^{-n}\n",
        "$$\n",
        "\n",
        "Using (see: Lecture ADSP, Slides 06)\n",
        "$$\\large\n",
        "\\Delta_N(n)= \\frac{1} {N } \\sum_{k = 0} ^ {N - 1} e^{j \\frac{2 π} {N} ∙ k ∙ n}\n",
        "$$\n",
        "\n",
        "this becomes\n",
        "\n",
        "$$\\large\n",
        "\\frac{1}{N} \\sum_{k=0} ^ {N-1} \\sum _{n=0} ^\\infty x(n) (e^{-j \\frac{2 \\pi}{ N} \\cdot k} \\cdot z)^{-n}\n",
        "$$\n",
        "\n",
        "$$\\large\n",
        "= \\frac{1}{N} \\sum_{k=0} ^{N-1} X(e^{-j \\frac{2 \\pi} {N} \\cdot k} \\cdot z)\n",
        "$$\n",
        "\n",
        "(using the z-Transform definition and replacing $z$ by $e^{-j \\frac{2 \\pi} {N} \\cdot k} \\cdot z$:)\n",
        "\n",
        "$$\\large\n",
        "X(e^{-j\\frac{2\\pi} {N} \\cdot k} \\cdot z)=\\sum _ {n=0} ^\\infty x(n)(e^{-j\\frac{2\\pi}{N} \\cdot k} \\cdot z)^{-n}\n",
        "$$\n",
        "\n",
        "or, in short,\n",
        "\n",
        "$$\\large\n",
        "X^d(z)=\\frac{1} {N} \\sum_ {k=0 }^{N-1} X( e^{-j \\frac{2 \\pi} {N} \\cdot k} \\cdot z)\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z2YqQJddNNk9"
      },
      "source": [
        "This is very similar to the Discrete Time Fourier transform formulation. We get a sum with aliasing components, just that we now don't have frequency shifts for the aliasing terms, but a **multiplication of their exponential functions** to z. Here we effectively shift the phase (or use rotation) of the complex number $z$ using this complex expoential. This also makes sense since the frequency information is contained in the phase of $z$, which we see if we replace $z=e^{j\\Omega}$.\n",
        "\n",
        "\n",
        "The next effect is the **removal or re-insertion of the zeros** from or into the signal. Let's again use our definition $y(m)=x^d(mN)$, meaning the y(m) is the signal without the zeros. Then the z-transform becomes,\n",
        "\n",
        "$$\\large\n",
        "Y(z)=\\sum _{ m=0} ^ \\infty y(m) z^{-m}=$$\n",
        "\n",
        "$$\\large\n",
        "=\\sum _{m=0} ^\\infty x^d(mN)z^{-m}\n",
        "$$\n",
        "\n",
        "Replacing the sum index m (the lower sampling rate) by the higher sampling rate n=mN, and observing that the sequence $x^d(n)$ contains the zeros, with $x^d(n)=0$ for $n\\neq mN$, this results in (using the index substitution $n=mN$)\n",
        "\n",
        "$$\\large\n",
        "=\\sum_{n=0} ^ \\infty x^d(n) z^{-n/N} =\n",
        "\\sum_{n=0}\n",
        "^\\infty x^d(n) (z^{1/N})^{-n}= X^d(z^{1/N})\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hHM9hgKeNNk-"
      },
      "source": [
        "### Modulation"
      ]
    },
    {
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        "id": "FX3QTucsNNk-",
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        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/qtwHRFxaGjo?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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      "source": [
        "Another very useful tool, is the **modulation**. This is the **multiplication** of our signal with a periodic function, for instance an exponential function. It can be written as\n",
        "\n",
        "$$\\large\n",
        "x_M(n):=x(n) \\cdot  e^{-j \\Omega_M \\cdot n}\n",
        "$$\n",
        "\n",
        "(where \"M\" denotes the modulation). Observe that the modulation function here has a periodicity of $2 \\pi/\\Omega_M$. Its z-transform hence becomes\n",
        "\n",
        "$$\\large\n",
        "X_M(z)=\\sum_ {n=0}^ \\infty x(n) \\cdot e^{-j\\Omega_M \\cdot n} \\cdot z^{-n}\n",
        "$$\n",
        "\n",
        "$$\\large\n",
        "X_M(z)=X( e^{j\\Omega_M} \\cdot z)\n",
        "$$\n",
        "\n",
        "here again we have this rotation (or phase shift) of z by an exponential factor.\n",
        "\n",
        "Observe that this has the effect of simply shifting the frequency response by $Ω_M$ , which can be seen by simply replacing z by $e^{j\\Omega}$ to obtain the frequency response."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sb5LFg-eNNk-"
      },
      "source": [
        "### Python example to modulating a speech signal:\n",
        "\n",
        "*Real-Time examples will not work inside cloud environments such as Google Colab and Binder*"
      ]
    },
    {
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        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/UvYIekLpnE4?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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    },
    {
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      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "uuyPoPqKNNk-",
        "outputId": "d0f8272c-4c14-4764-e7c0-142ed75cfddc",
        "colab": {
          "referenced_widgets": [
            "09976d6ec29240d191a1f51de7f09f74",
            "58ae120a794b4224822abf544115994f"
          ]
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      },
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              "ToggleButton(value=False, description='Stop')"
            ]
          },
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        },
        {
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              "Checkbox(value=False, description='Modulation')"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "PyAudio terminated...\n"
          ]
        }
      ],
      "source": [
        "\"\"\"\n",
        "PyAudio Example: Make a modulation between input and output (i.e., record a\n",
        "few samples, modulate them with a sine, and play them back immediately).\n",
        "Using block-wise processing instead of a for loop\n",
        "Gerald Schuller, Octtober 2014\n",
        "\n",
        "Updated and Ported to Jupyter Notebooks by: Renato Profeta, July 2020\n",
        "\"\"\"\n",
        "\n",
        "import time\n",
        "import numpy as np\n",
        "from pyaudio import PyAudio, paFloat32, paContinue, paInt16, paComplete\n",
        "from ipywidgets import ToggleButton, Checkbox\n",
        "import threading\n",
        "\n",
        "sampling_on=False\n",
        "\n",
        "button_stop= ToggleButton(description='Stop')\n",
        "box_sampling = Checkbox(False, description='Modulation')\n",
        "\n",
        "def on_button_stop(change):\n",
        "    if change['new']==True:\n",
        "        stream.stop_stream()\n",
        "        stream.close()\n",
        "        pa.terminate()\n",
        "        button_stop.disabled=True\n",
        "        print('PyAudio terminated...')\n",
        "button_stop.observe(on_button_stop, 'value')\n",
        "display(button_stop)\n",
        "\n",
        "def box_sampling_changed(box_sampling):\n",
        "    global SamplingOn\n",
        "    if box_sampling['new']:\n",
        "        SamplingOn=True\n",
        "    else:\n",
        "        SamplingOn=False\n",
        "box_sampling.observe(box_sampling_changed, names='value')\n",
        "display(box_sampling)\n",
        "\n",
        "s=np.sin(np.pi/128*4*np.arange(0,1024))\n",
        "SamplingOn=False\n",
        "\n",
        "\n",
        "def callback(in_data, frame_count, time_info, flag):\n",
        "    global SamplingOn\n",
        "    audio_data = np.frombuffer(in_data, dtype=np.int16).astype('float')\n",
        "    audio_data_s = audio_data\n",
        "    if SamplingOn:\n",
        "        audio_data_s=audio_data*s\n",
        "    if button_stop.value==True:\n",
        "        return (audio_data_s.astype('int16'), paComplete)\n",
        "    return (audio_data_s.astype('int16'), paContinue)\n",
        "\n",
        "pa = PyAudio()\n",
        "\n",
        "stream = pa.open(format = paInt16,\n",
        "                 channels = 1,\n",
        "                 rate = 32000,\n",
        "                 output = True,\n",
        "                 input = True,\n",
        "                 frames_per_buffer = 1024,\n",
        "                 stream_callback = callback)\n",
        "\n",
        "\n",
        "def keep_alive(button_stop):\n",
        "    while stream.is_active():\n",
        "        if button_stop.value==True:\n",
        "            break\n",
        "        time.sleep(0.1)\n",
        "\n",
        "# Create a Thread for function\n",
        "thread = threading.Thread(target=keep_alive, args=(button_stop,))\n",
        "stream.start_stream()\n",
        "thread.start()"
      ]
    },
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              "<IPython.core.display.HTML object>"
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      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/upoWSbQ4ZA4?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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      "source": [
        "An intersting case is obtained if we set $\\Omega_M=\\pi$. Then the modulating function is just a sequence of +1,-1,+1,..., and multiplying this with our signal results in a frequency shift of $\\pi$ . If we have a real valued low pass signal, for instance, this will then be shifted by $\\pi$ , and we will obtain a high pass. In this\n",
        "way we can turn the impulse response of a low pass into a high pass, vice versa.\n",
        "\n",
        "<center>\n",
        "    <br>\n",
        "    <img src='https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/ac_01_modulation.png' width='800'>\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bzTFvHOTNNk-"
      },
      "source": [
        "Another important tool is the **reversal of the ordering** of a finite length signal sequence, with length L (meaning x(n) is non-zero only for n=0,... , L−1 ):\n",
        "\n",
        "$$\\large\n",
        "x_r(n):=x(L-1-n)$$\n",
        "\n",
        "Its z-transform is:\n",
        "\n",
        "$$\\large\n",
        "X_r(z) = \\sum_{n=0}^{\\infty}x(L-1-n)\\cdot z^{-1}$$\n",
        "\n",
        "we can now reverse the order of the summation (of course without affecting the result) by starting at the highest index, going to the lowest, replacing the index n by the expression L−1−n' (index substitution):\n",
        "\n",
        "$$\\large\n",
        "X_r(z)=\\sum_{n'=0}^{\\infty} x(n') \\cdot z^{-(L-1-n')} = z^{-(L-1)}\\cdot X(z^{-1})$$\n",
        "\n",
        "or, in short,\n",
        "\n",
        "$$\\large\n",
        "X_r(z) = z^{-(L-1)}\\cdot X(z^{-1})$$\n",
        "\n",
        "So what we obtain is the inverse of z in the z-transform (which signifies the time reversal), and a factor of $z^{-(L-1)}$, which is simply a delay of L-1 samples!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wvnu5EB9NNk_"
      },
      "source": [
        "## Mid-rise and Mid-tread quantization"
      ]
    },
    {
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        "id": "Q4SrluJbNNk_",
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      "outputs": [
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        "Depending on if the quantizer has the input voltage 0 at the center of a quantization interval or on the boundary of that interval, we call the quantizer a mid-tread or a mid rise quantiser, as illustrated in the following picture:\n",
        "\n",
        "<center><img src=\"https://raw.githubusercontent.com/TUIlmenauAMS/AudioCoding_Tutorials/main/images/rise_tread_quantizers.png\"></center>\n",
        "<font size=\"2\">      \n",
        "(From:http://eeweb.poly.edu/~yao/EE3414/quantization.pdf)\n",
        "</font>\n",
        "\n",
        "Here, $Q_i(f)$ is the index after quantization (which is then encoded and sent to the receiver), and Q(f) is the de-quantization, which produces the quantized reconstructed value at the receiver. Q is the quantization step size, which is identical to $\\Delta$ in the plots.\n",
        "\n",
        "We define the difference between the reverse quantized (through encoder and decoder) and the original signal ( e=Q(f )−f ) as **\"quantization error\".**\n",
        "\n",
        "The resulting quantisation error power in both cases is:\n",
        "\n",
        "$$ \\large E(e^2)=\\frac{\\Delta^2}{12} $$\n"
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        "\"\"\"\n",
        "PyAudio Example: Make a quantization between input and output\n",
        "(i.e., record a few samples, quatize them with a mid-tread or\n",
        "mid-rise quantizer, and play them back immediately).\n",
        "Using block-wise processing instead of a for loop\n",
        "Gerald Schuller, Octtober 2014\n",
        "\n",
        "Modified to Jupyter Notebook by Renato Profeta, October 2019\n",
        "\"\"\"\n",
        "# Imports\n",
        "import pyaudio\n",
        "import struct\n",
        "import numpy as np\n",
        "from ipywidgets import ToggleButton, Dropdown, Button, BoundedIntText, Label\n",
        "from ipywidgets import HBox, interact\n",
        "import threading\n",
        "\n",
        "# Parameters\n",
        "CHUNK = 5000 #Blocksize\n",
        "FORMAT = pyaudio.paInt16 #conversion format for PyAudio stream\n",
        "CHANNELS = 1\n",
        "RATE = 32000  #Sampling Rate in Hz\n",
        "\n",
        "\n",
        "# Quantization Bit-Depth\n",
        "N=8\n",
        "quant_type='Mid-Tread'\n",
        "\n",
        "\n",
        "# Quantization Application\n",
        "def quantization_example(toggle_run):\n",
        "    global N, quant_type\n",
        "    while(True):\n",
        "        if toggle_run.value==True:\n",
        "            break\n",
        "        #Reading from audio input stream into data with block length \"CHUNK\":\n",
        "        data_stream = stream.read(CHUNK)\n",
        "        #Convert from stream of bytes to a list of short integers\n",
        "        #(2 bytes here) in \"samples\":\n",
        "        shorts = (struct.unpack( 'h' * CHUNK, data_stream ));\n",
        "        samples=np.array(list(shorts),dtype=float);\n",
        "\n",
        "        #start block-wise signal processing:\n",
        "        q=int((2**15-(-2**15))/(2**N))\n",
        "\n",
        "        if quant_type=='Mid-Tread':\n",
        "            #Mid Tread quantization:\n",
        "            indices=np.round(samples/q)\n",
        "            #de-quantization:\n",
        "            samples=indices*q\n",
        "        else:\n",
        "            #Mid -Rise quantizer:\n",
        "            indices=np.floor(samples/q)\n",
        "            #de-quantization:\n",
        "            samples=(indices*q+q/2).astype(int)\n",
        "            #end signal processing\n",
        "\n",
        "        #converting from short integers to a stream of bytes in \"data\":\n",
        "        #play out samples:\n",
        "        samples=np.clip(samples, -2**15,2**15)\n",
        "        samples=samples.astype(np.int16)\n",
        "        data=struct.pack('h' * len(samples), *samples);\n",
        "        #Writing data back to audio output stream:\n",
        "        stream.write(data, CHUNK)\n",
        "\n",
        "# GUI\n",
        "toggle_run = ToggleButton(description='Stop')\n",
        "button_start = Button(description='Start')\n",
        "dropdown_type = Dropdown(\n",
        "    options=['Mid-Tread', 'Mid-Rise'],\n",
        "    value='Mid-Tread',\n",
        "    description='Quantization Type:',\n",
        "    disabled=False,\n",
        ")\n",
        "bitdepth_int = BoundedIntText(\n",
        "    value=8,\n",
        "    min=2,\n",
        "    max=16,\n",
        "    step=1,\n",
        "    description='Bit-Depth:',\n",
        "    disabled=False\n",
        ")\n",
        "\n",
        "q=int((2**15-(-2**15))/(2**N))\n",
        "stepsize_label = Label(value=\"Stepsize: {:d}\".format(q))\n",
        "\n",
        "def start_button(button_start):\n",
        "    thread.start()\n",
        "    button_start.disabled=True\n",
        "button_start.on_click(start_button)\n",
        "\n",
        "\n",
        "def on_click_toggle_run(change):\n",
        "    if change['new']==False:\n",
        "        stream.stop_stream()\n",
        "        stream.close()\n",
        "        p.terminate()\n",
        "        plt.close()\n",
        "toggle_run.observe(on_click_toggle_run, 'value')\n",
        "\n",
        "def inttext_bitdepth_changed(bitdepth_int):\n",
        "    global N, q\n",
        "    if bitdepth_int['new']:\n",
        "        N=bitdepth_int['new']\n",
        "        stepsize_label.value=\"Stepsize: {:d}\".format(int((2**15-(-2**15))/(2**N)))\n",
        "bitdepth_int.observe(inttext_bitdepth_changed, names='value')\n",
        "\n",
        "def dropdown_type_changed(dropdown_type):\n",
        "    global quant_type\n",
        "    if dropdown_type['new']:\n",
        "        quant_type=dropdown_type['new']\n",
        "dropdown_type.observe(dropdown_type_changed, names='value')\n",
        "\n",
        "\n",
        "box_buttons = HBox([button_start,toggle_run])\n",
        "box_controls = HBox([bitdepth_int, dropdown_type,stepsize_label])\n",
        "\n",
        "# Create a Thread for run_spectrogram function\n",
        "thread = threading.Thread(target=quantization_example, args=(toggle_run,))\n",
        "\n",
        "# Start Audio Stream\n",
        "# Create\n",
        "p = pyaudio.PyAudio()\n",
        "\n",
        "stream = p.open(format=FORMAT,\n",
        "                channels=CHANNELS,\n",
        "                rate=RATE,\n",
        "                input=True,\n",
        "                output=True,\n",
        "                frames_per_buffer=CHUNK)\n",
        "\n",
        "\n",
        "\n",
        "input_data = stream.read(CHUNK)\n",
        "samples = np.frombuffer(input_data,np.int16)\n",
        "\n",
        "display(box_buttons)\n",
        "display(box_controls)"
      ]
    },
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      "source": [
        "Observe: Both quantizers distort the signal audibly.\n",
        "\n",
        "The mid-tread quantizer does not let small signals through, it rounds them to zero, which also saves bits. The mid-rise quantizer does let small signals through, since it quantizes small values either to Q/2 or -Q/2, but distorted, and it also cost some bit rate, since these values need to be encoded.\n",
        "\n",
        "In General you want to make the quantization step size bigger to save bit rate, but only big enough to avoid audible distortions."
      ]
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