#
# Fast discrete cosine transform algorithms (Python)
#
# Copyright (c) 2020 Project Nayuki. (MIT License)
# https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
#
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#
import cmath, fft
# DCT type II, unscaled
def transform(vector):
temp = vector[ : : 2] + vector[-1 - len(vector) % 2 : : -2]
temp = fft.transform(temp, False)
factor = -1j * cmath.pi / (len(vector) * 2)
return [(val * cmath.exp(i * factor)).real for (i, val) in enumerate(temp)]
# DCT type III, unscaled
def inverse_transform(vector):
n = len(vector)
factor = -1j * cmath.pi / (len(vector) * 2)
temp = [(val if i > 0 else val / 2) * cmath.exp(i * factor)
for (i, val) in enumerate(vector)]
temp = fft.transform(temp, False)
temp = [val.real for val in temp]
result = [None] * n
result[ : : 2] = temp[ : (n + 1) // 2]
result[-1 - len(vector) % 2 : : -2] = temp[(n + 1) // 2 : ]
return result