Computation of an odd-length DCT from a real-valued DFT of the samelength |
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Authors: | Heideman MT |
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Affiliation: | Etak Inc., Menlo Park, CA; |
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Abstract: | The discrete cosine transform (DCT) is often computed from a discrete Fourier transform (DFT) of twice or four times the DCT length. DCT algorithms based on identical-length DFT algorithms generally require additional arithmetic operations to shift the phase of the DCT coefficients. It is shown that a DCT of odd length can be computed by an identical-length DFT algorithm, by simply permuting the input and output sequences. Using this relation, odd-length DCT modules for a prime factor DCT are derived from corresponding DFT modules. The multiplicative complexity of the DCT is then derived in terms of DFT complexities |
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