Durbin-Levinson One Step

Problem

Advance the Durbin-Levinson recursion by one order. Given the previous order coefficients and the autocorrelation list rho = [rho(0), ..., rho(k)] with k = len(coeffs) + 1, compute the reflection coefficient kappa = (rho(k) - sum a_j * rho(k-j)) / (1 - sum a_j * rho(j)), where sums run over j = 1..k-1. Then return the updated coefficients with kappa appended, using a_j - kappa * a_{k-j} for the existing entries.

If the denominator is zero, use kappa = 0.0.

Hint

The appended value is the new reflection coefficient; rho[0] is assumed to be 1.

Test cases

case 1

in: [[],[1,0.5]]

expected: [0.5]

case 2

in: [[0.5],[1,0.5,0.25]]

expected: [0.5,0]

case 3

in: [[0.5],[1,0.5,0.3]]

expected: [0.4666666666666667,0.06666666666666665]

case 4

in: [[0.6],[1,0.6,0.3]]

expected: [0.65625,-0.09375]

Starter codePython

def durbin_levinson_step(coeffs, rho):
    # Your code here
    pass

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