2 # Fast discrete cosine transform algorithms (Python)
4 # Copyright (c) 2020 Project Nayuki. (MIT License)
5 # https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
7 # Permission is hereby granted, free of charge, to any person obtaining a copy of
8 # this software and associated documentation files (the "Software"), to deal in
9 # the Software without restriction, including without limitation the rights to
10 # use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
11 # the Software, and to permit persons to whom the Software is furnished to do so,
12 # subject to the following conditions:
13 # - The above copyright notice and this permission notice shall be included in
14 # all copies or substantial portions of the Software.
15 # - The Software is provided "as is", without warranty of any kind, express or
16 # implied, including but not limited to the warranties of merchantability,
17 # fitness for a particular purpose and noninfringement. In no event shall the
18 # authors or copyright holders be liable for any claim, damages or other
19 # liability, whether in an action of contract, tort or otherwise, arising from,
20 # out of or in connection with the Software or the use or other dealings in the
27 # DCT type II, unscaled.
28 # See: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II
29 def transform(vector
):
31 factor
= math
.pi
/ len(vector
)
32 for i
in range(len(vector
)):
34 for (j
, val
) in enumerate(vector
):
35 sum += val
* math
.cos((j
+ 0.5) * i
* factor
)
40 # DCT type III, unscaled.
41 # See: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-III
42 def inverse_transform(vector
):
44 factor
= math
.pi
/ len(vector
)
45 for i
in range(len(vector
)):
47 for j
in range(1, len(vector
)):
48 sum += vector
[j
] * math
.cos(j
* (i
+ 0.5) * factor
)