Dynamic Harmonic Regression

Problem

Fit a harmonic regression y = a + b * cos(2*pi*f*t) + c * sin(2*pi*f*t) by ordinary least squares and return the amplitude sqrt(b^2 + c^2).

Return 0.0 when the series has fewer than three points or the normal equations are singular.

Hint

The amplitude is the Euclidean norm of the cosine and sine coefficients.

case 1

in: [[1,0,-1,0],0.25]

expected: 1

case 2

in: [[0,1,0,-1],0.25]

expected: 1

case 3

in: [[1,2,3,4,5],0.1]

expected: 1.9919186279062238

case 4

in: [[5,5,5,5],0.25]

expected: 1.1102230246251565e-16

Starter codePython

import math
def dynamic_harmonic_regression_coefficient(series, freq):
    # Your code here
    pass

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