MediumTime Seriests-064

Periodogram Bin

Problem

Compute the periodogram at a single frequency bin k: I(k) = (1/n) * abs(sum over t of x[t] * exp(-2*pi*i*k*t/n))^2.

Return 0.0 if k is outside the range 0 to n-1.

Hint

For a constant series all nonzero bins are (numerically) zero.

case 1

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

expected: 0.25

case 2

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

expected: 7.498798913309287e-33

case 3

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

expected: 2

case 4

in: [[1,2,3],0]

expected: 12

Starter codePython

import math
def periodogram_bin(series, k):
    # Your code here
    pass

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