Spectral Density Value

Problem

Evaluate the truncated spectral density at frequency f from an autocorrelation list acf = [rho(0), ..., rho(K)]: S(f) = rho(0) + 2 * sum over k = 1..K of rho(k) * cos(2 * pi * f * k).

Return the value as a number.

Hint

The density at frequency 0 is the sum of all autocorrelations with weight 2 on positive lags.

Test cases

case 1

in: [[1,0.5],0]

expected: 2

case 2

in: [[1,0.5],0.5]

expected: 0

case 3

in: [[1,0.25,0.1],0.25]

expected: 0.8

case 4

in: [[1],0.3]

expected: 1

Starter codePython

import math
def spectral_density(acf, f):
    # Your code here
    pass

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