#
# Fast discrete cosine transform algorithms (Python)
#
# Copyright (c) 2017 Project Nayuki. (MIT License)
# https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of
# this software and associated documentation files (the "Software"), to deal in
# the Software without restriction, including without limitation the rights to
# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
# the Software, and to permit persons to whom the Software is furnished to do so,
# subject to the following conditions:
# - The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# - The Software is provided "as is", without warranty of any kind, express or
# implied, including but not limited to the warranties of merchantability,
# fitness for a particular purpose and noninfringement. In no event shall the
# authors or copyright holders be liable for any claim, damages or other
# liability, whether in an action of contract, tort or otherwise, arising from,
# out of or in connection with the Software or the use or other dealings in the
# Software.
#
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 / 2.0) * 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