# # 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 math # DCT type II, unscaled. # See: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II def transform(vector): result = [] factor = math.pi / len(vector) for i in range(len(vector)): sum = 0.0 for (j, val) in enumerate(vector): sum += val * math.cos((j + 0.5) * i * factor) result.append(sum) return result # DCT type III, unscaled. # See: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-III def inverse_transform(vector): result = [] factor = math.pi / len(vector) for i in range(len(vector)): sum = vector[0] / 2 for j in range(1, len(vector)): sum += vector[j] * math.cos(j * (i + 0.5) * factor) result.append(sum) return result