#
# 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 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] / 2.0
for j in range(1, len(vector)):
sum += vector[j] * math.cos(j * (i + 0.5) * factor)
result.append(sum)
return result