#
# Fast discrete cosine transform algorithms (Python)
#
# Copyright (c) 2018 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] /= 2.0
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