Spectral Entropy

Problem

Compute the normalized spectral entropy of a series. Take the periodogram powers at bins k = 0..n//2, normalize them into a distribution, compute the Shannon entropy in nats, and divide by log(number of bins).

Return 0.0 when there are fewer than two points or total power is zero. A pure tone gives near 0; white noise gives near 1.

Hint

A flat spectrum maximizes entropy; a single spike minimizes it.

Test cases

case 1

in: [[1,2,3,4]]

expected: 0.37201270119579155

case 2

in: [[5,5,5,5]]

expected: 3.8340693177808697e-31

case 3

in: [[0,1,0,1]]

expected: 0.6309297535714574

case 4

in: [[1,-1,1,-1]]

expected: 1.2859084648443834e-31

Starter codePython

import math
def spectral_entropy(series):
    # Your code here
    pass

4 test cases · run your code against them in the editor