Parseval Energy Check

Problem

Parseval's theorem says the time-domain energy of a length-N sequence equals (1/N) times the frequency-domain energy, where X[k] = sum of x[n]*e^(-2*pi*i*k*n/N).

Compute the DFT with real arithmetic and return (1/N) * sum of |X[k]|^2, which equals the sum of x[n]^2.

Hint

Expand the squared magnitude of the DFT and use the orthogonality of complex exponentials.

Test cases

case 1

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

expected: 1

case 2

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

expected: 4

case 3

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

expected: 4

case 4

in: [[0.5,0.5]]

expected: 0.5

Starter codePython

def parseval_energy(x):
    # Your code here
    pass

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