A fast cosine transform in one and two dimensions

1980/02/01 by J. Makhoul · 5 citations
Computer Science · Engineering · Mathematics · #Digital Filter Design and Implementation #Advancements in PLL and VCO Technologies #Numerical Methods and Algorithms #Discrete cosine transform #Discrete Fourier transform (general) #Discrete sine transform #Fast Fourier transform #Discrete Hartley transform #Algorithm #Non-uniform discrete Fourier transform #Mathematics #Point (geometry) #Sine and cosine transforms #Fourier transform #Modified discrete cosine transform #Trigonometric functions #Fractional Fourier transform #Extension (predicate logic) #Signal processing #Arithmetic #Discrete mathematics #Computer science #Digital signal processing #Mathematical analysis #Fourier analysis #Artificial intelligence #Geometry #Image (mathematics)

paper · doi:10.1109/tassp.1980.1163351

openalex publication_date 1980/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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 ofN log₂ Nreal multiplications. The method is then extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.

Citations

• Discrete Cosine Transform

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• Discrete cosine transform [wikipedia]