DCT Apply

Problem

Apply the orthonormal DCT-II transform to vector x of length n:

out[k] = alpha_k * sum_i x[i] * cos(pi * (2i + 1) * k / (2n))

with alpha_0 = sqrt(1/n) and alpha_k = sqrt(2/n) for k > 0.

Hint

The DCT is a real orthogonal transform; the k = 0 coefficient is the mean times sqrt(n).

case 1

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

expected: [0.5,0.6532814824381883,0.5,0.27059805007309856]

case 2

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

expected: [2,0,0,0]

case 3

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

expected: [5,-2.230442497387663,0,-0.15851266778110815]

case 4

in: [[1,0]]

expected: [0.7071067811865476,0.7071067811865476]

Starter codePython

def dct_apply(x):
    # Your code here
    pass

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