From 3ab39e8207ee95e353a0d326a8678d2429298e0d Mon Sep 17 00:00:00 2001
From: mhostetter <matthostetter@gmail.com>
Date: Sun, 19 Nov 2023 12:05:49 -0500
Subject: [PATCH 1/3] Add `sdr.hamming()`

Closes #63
---
 src/sdr/_measurement/_distance.py | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/src/sdr/_measurement/_distance.py b/src/sdr/_measurement/_distance.py
index 5b7dda8ad..2783ccb1b 100644
--- a/src/sdr/_measurement/_distance.py
+++ b/src/sdr/_measurement/_distance.py
@@ -36,3 +36,32 @@ def euclidean(
     y = np.asarray(y)
     d = np.sqrt(np.sum(np.abs(x - y) ** 2, axis=axis))
     return d
+
+
+@export
+def hamming(
+    x: npt.NDArray[np.int_],
+    y: npt.NDArray[np.int_],
+    axis: int | tuple[int, ...] | None = None,
+) -> npt.NDArray[np.int_]:
+    r"""
+    Measures the Hamming distance between two signals $x[n]$ and $y[n]$.
+
+    $$d = \sum_{n=0}^{N-1} x[n] ^ y[n]$$
+
+    Arguments:
+        x: The time-domain signal $x[n]$.
+        y: The time-domain signal $y[n]$.
+        axis: Axis or axes along which to compute the distance. The default is `None`, which computes the distance
+            across the entire array.
+
+    Returns:
+        The Hamming distance between $x[n]$ and $y[n]$.
+
+    Group:
+        measurement-distance
+    """
+    x = np.asarray(x)
+    y = np.asarray(y)
+    d = np.sum(np.bitwise_xor(x, y), axis=axis)
+    return d

From 306fd46bd3ce4d9742588bc5ca96ba5d1b3f6a2c Mon Sep 17 00:00:00 2001
From: mhostetter <matthostetter@gmail.com>
Date: Sun, 19 Nov 2023 12:06:09 -0500
Subject: [PATCH 2/3] Add unit tests for `hamming()`

---
 tests/measurements/test_hamming.py | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)
 create mode 100644 tests/measurements/test_hamming.py

diff --git a/tests/measurements/test_hamming.py b/tests/measurements/test_hamming.py
new file mode 100644
index 000000000..80e4f5fcc
--- /dev/null
+++ b/tests/measurements/test_hamming.py
@@ -0,0 +1,24 @@
+import numpy as np
+
+import sdr
+
+X = np.array([[6, 5, 0, 0, 5], [0, 1, 5, 0, 3], [4, 3, 3, 0, 5]])
+Y = np.array([[7, 5, 2, 4, 0], [0, 0, 4, 1, 5], [5, 0, 7, 5, 6]])
+
+
+def test_axis_none():
+    d = sdr.hamming(X, Y)
+    assert d.shape == ()
+    assert d == 37
+
+
+def test_axis_0():
+    d = sdr.hamming(X, Y, axis=0)
+    assert d.shape == (5,)
+    assert np.allclose(d, [2, 4, 7, 10, 14])
+
+
+def test_axis_1():
+    d = sdr.hamming(X, Y, axis=1)
+    assert d.shape == (3,)
+    assert np.allclose(d, [12, 9, 16])

From 4d9f3d6121ac026139e6c592e607edbbc065bc0f Mon Sep 17 00:00:00 2001
From: mhostetter <matthostetter@gmail.com>
Date: Sun, 19 Nov 2023 12:10:07 -0500
Subject: [PATCH 3/3] Fix LaTeX xor symbol

---
 src/sdr/_measurement/_distance.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sdr/_measurement/_distance.py b/src/sdr/_measurement/_distance.py
index 2783ccb1b..329de7ef1 100644
--- a/src/sdr/_measurement/_distance.py
+++ b/src/sdr/_measurement/_distance.py
@@ -47,7 +47,7 @@ def hamming(
     r"""
     Measures the Hamming distance between two signals $x[n]$ and $y[n]$.
 
-    $$d = \sum_{n=0}^{N-1} x[n] ^ y[n]$$
+    $$d = \sum_{n=0}^{N-1} x[n] \oplus y[n]$$
 
     Arguments:
         x: The time-domain signal $x[n]$.