Quantized Gaussian Entropy

Problem

Approximate the entropy in bits of a Gaussian with variance var after uniform quantization with step size step:

H ~ 0.5 * log2(2 * pi * e * var) - log2(step)

That is the differential entropy minus the quantization resolution.

Hint

Finer quantization (smaller step) increases the discrete entropy.

case 1

in: [1,1]

expected: 2.047095585180641

case 2

in: [1,0.5]

expected: 3.047095585180641

case 3

in: [4,1]

expected: 3.047095585180641

case 4

in: [1,2]

expected: 1.047095585180641

Starter codePython

import math
def quantized_gaussian_entropy(var, step):
    # Your code here
    pass

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