# # 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. Algorithm by Byeong Gi Lee, 1984. # See: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.118.3056&rep=rep1&type=pdf#page=34 def transform(vector): n = len(vector) if n == 1: return list(vector) elif n == 0 or n % 2 != 0: raise ValueError() else: half = n // 2 alpha = [(vector[i] + vector[-(i + 1)]) for i in range(half)] beta = [(vector[i] - vector[-(i + 1)]) / (math.cos((i + 0.5) * math.pi / n) * 2.0) for i in range(half)] alpha = transform(alpha) beta = transform(beta ) result = [] for i in range(half - 1): result.append(alpha[i]) result.append(beta[i] + beta[i + 1]) result.append(alpha[-1]) result.append(beta [-1]) return result # DCT type III, unscaled. Algorithm by Byeong Gi Lee, 1984. # See: https://www.nayuki.io/res/fast-discrete-cosine-transform-algorithms/lee-new-algo-discrete-cosine-transform.pdf def inverse_transform(vector, root=True): if root: vector = list(vector) vector[0] /= 2 n = len(vector) if n == 1: return vector elif n == 0 or n % 2 != 0: raise ValueError() else: half = n // 2 alpha = [vector[0]] beta = [vector[1]] for i in range(2, n, 2): alpha.append(vector[i]) beta.append(vector[i - 1] + vector[i + 1]) inverse_transform(alpha, False) inverse_transform(beta , False) for i in range(half): x = alpha[i] y = beta[i] / (math.cos((i + 0.5) * math.pi / n) * 2) vector[i] = x + y vector[-(i + 1)] = x - y return vector