added convolution

DIRECTORY.md

@@ -724,6 +724,7 @@
   * [Collatz Sequence](maths/collatz_sequence.py)
   * [Combinations](maths/combinations.py)
   * [Continued Fraction](maths/continued_fraction.py)
+  * [Convolve 1D](maths/convolve_1d.py)
   * [Decimal Isolate](maths/decimal_isolate.py)
   * [Decimal To Fraction](maths/decimal_to_fraction.py)
   * [Dodecahedron](maths/dodecahedron.py)
@@ -876,6 +877,7 @@
   * [Two Pointer](maths/two_pointer.py)
   * [Two Sum](maths/two_sum.py)
   * [Volume](maths/volume.py)
+  * [Weighted Average](maths/weighted_average.py)
   * [Zellers Congruence](maths/zellers_congruence.py)
 
 ## [Matrix](matrix)

maths/convolve_1d.py

@@ -0,0 +1,62 @@
+from dataclasses import dataclass, field
+from math import floor
+
+# discrete_convolution
+"""
+    * Calculate the discrete convolution of two
+        linear discrete sets
+    https://en.wikipedia.org/wiki/Convolution
+"""
+
+
+@dataclass
+class Signal:
+    """
+    A discrete representation of a signal as a n-dimensional vector
+
+    >>> Signal([1.0,3.0,2.0,-1.0])
+    Signal(signal=[1.0, 3.0, 2.0, -1.0], n=4)
+    """
+
+    signal: list[float] = field(default_factory=list)
+    n: int = 0
+
+    def __post_init__(self) -> None:
+        for i in self.signal:
+            if not isinstance(i, (float, int)):
+                raise TypeError("vector must be a list of numeric values.")
+            else:
+                self.n += 1
+
+
+@dataclass
+class DiscreteConvolve1D:
+    """
+    1D discrete convolution between two linear signals
+
+    >>> s1 = Signal([1,2,3,4,5])
+    >>> s2 = Signal([1,-1,2,-3])
+    >>> DiscreteConvolve1D(s1,s2) # doctest: +NORMALIZE_WHITESPACE
+    DiscreteConvolve1D(kern=Signal(signal=[1, 2, 3, 4, 5], n=5),
+    sig=Signal(signal=[1, -1, 2, -3], n=4))
+    """
+
+    kern: Signal = field(default_factory=Signal)
+    sig: Signal = field(default_factory=Signal)
+
+    @property
+    def convolve_1d(self) -> Signal:
+        conv = Signal()
+        for i in range(self.sig.n):
+            conv.signal.append(0)
+            for j in range(self.kern.n):
+                if (
+                    i + j - floor(self.kern.n / 2) < 0
+                    or i + j - floor(self.kern.n / 2) >= self.sig.n
+                ):
+                    sig_val = 0.0
+                else:
+                    sig_val = float(self.sig.signal[i + j - floor(self.kern.n / 2)])
+                conv.signal[i] += self.kern.signal[j] * sig_val
+            conv.n += 1
+        return conv