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A fast cosine transform in one and two dimensions

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1 Author(s)
Makhoul, J. ; Bolt Beranek and Newman, Inc., Cambridge, MA

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 N \log _{2} N real multiplications. The method is then extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:28 ,  Issue: 1 )