# # Fast discrete cosine transform algorithms (Python) # # Copyright (c) 2020 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) * 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