#
# 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
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# - The Software is provided "as is", without warranty of any kind, express or
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# 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