[python] Moving average or running mean

A new convolve recipe was merged into Python 3.10.

Given


import collections, operator

from itertools import chain, repeat


size = 3 + 1
kernel = [1/size] * size                                              

Code

def convolve(signal, kernel):
    # See:  https://betterexplained.com/articles/intuitive-convolution/
    # convolve(data, [0.25, 0.25, 0.25, 0.25]) --> Moving average (blur)
    # convolve(data, [1, -1]) --> 1st finite difference (1st derivative)
    # convolve(data, [1, -2, 1]) --> 2nd finite difference (2nd derivative)
    kernel = list(reversed(kernel))
    n = len(kernel)
    window = collections.deque([0] * n, maxlen=n)
    for x in chain(signal, repeat(0, n-1)):
        window.append(x)
        yield sum(map(operator.mul, kernel, window))

Demo

list(convolve(range(1, 6), kernel))
# [0.25, 0.75, 1.5, 2.5, 3.5, 3.0, 2.25, 1.25]

Details

A convolution is a general mathematical operation that can be applied to moving averages. This idea is, given some data, you slide a subset of data (window) as a "mask" or "kernel" across the data, carrying out a particular mathematical operation over each window. In the case of moving averages, the kernel is the average:

enter image description here

This recipe is a simple approach that is almost implemented as a Python module. In time, you can install more_itertools, a popular third-party package, to directly use this implementation.

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