Haar Wavelet Step

Problem

Apply one level of the orthonormal Haar wavelet transform to a vector of even length:

coarse[i] = (x[2i] + x[2i+1]) / sqrt(2), detail[i] = (x[2i] - x[2i+1]) / sqrt(2)

Return the coarse coefficients followed by the detail coefficients.

Hint

The transform is orthogonal, so energy is preserved between the coarse and detail parts.

case 1

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

expected: [1.4142135623730951,1.4142135623730951,0,0]

case 2

in: [[1,0]]

expected: [0.7071067811865476,0.7071067811865476]

case 3

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

expected: [2.1213203435596424,4.949747468305833,-0.7071067811865476,-0.7071067811865476]

case 4

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

expected: [0,0,0,0]

Starter codePython

def haar_step(x):
    # Your code here
    pass

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