Add equations for differential codes

mhostetter · Nov 19, 2023 · b6f3921 · b6f3921
1 parent 4eed74c
commit b6f3921
Showing 1 changed file with 6 additions and 2 deletions.
diff --git a/src/sdr/_modulation/_symbol_encoding.py b/src/sdr/_modulation/_symbol_encoding.py
@@ -11,9 +11,11 @@
 
 @export
 def diff_encode(x: npt.ArrayLike, y_prev: int = 0) -> npt.NDArray[np.int_]:
-    """
+    r"""
     Differentially encodes the input data $x[k]$.
 
+    $$y[k] = x[k] \oplus y[k-1]$$
+
     Args:
         x: The input uncoded data $x[k]$.
         y_prev: The previous value of the output encoded data $y[k-1]$.
@@ -66,9 +68,11 @@ def diff_encode(x: npt.ArrayLike, y_prev: int = 0) -> npt.NDArray[np.int_]:
 
 @export
 def diff_decode(y: npt.ArrayLike, y_prev: int = 0) -> npt.NDArray[np.int_]:
-    """
+    r"""
     Differentially decodes the input data $y[k]$.
 
+    $$x[k] = y[k] \oplus y[k-1]$$
+
     Arguments:
         y: The input encoded data $y[k]$.
         y_prev: The previous value of the encoded data $y[k-1]$.