On Computing the Discrete Cosine Transform

Haralick has shown that the discrete cosine transform of N points can be computed more rapidly by taking two N-point fast Fourier transforms (FFT´s) than by taking one 2N-point FFT as Ahmed had proposed. In this correspondence, we show that if Haralick had made use of the fact that the FFT´s of real sequences can be computed more rapidly than general FFT´s, the result would have been reversed. A modified algorithm is also presented.