DocumentCode :
1093477
Title :
A fast cosine transform in one and two dimensions
Author :
Makhoul, John
Author_Institution :
Bolt Beranek and Newman, Inc., Cambridge, MA
Volume :
28
Issue :
1
fYear :
1980
fDate :
2/1/1980 12:00:00 AM
Firstpage :
27
Lastpage :
34
Abstract :
The discrete cosine transform (DCT) of an N-point real signal is derived by taking the discrete Fourier transform (DFT) of a 2N-point even extension of the signal. It is shown that the same result may be obtained using only an N-point DFT of a reordered version of the original signal, with a resulting saving of 1/2. If the fast Fourier transform (FFT) is used to compute the DFT, the result is a fast cosine transform (FCT) that can be computed using on the order of 
real multiplications. The method is then extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.
real multiplications. The method is then extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.Keywords :
Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Fast Fourier transforms; Forward contracts; Fourier transforms; Helium; Image processing; Software algorithms; Speech processing;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/TASSP.1980.1163351
Filename :
1163351
Link To Document :
