Efficient index mapping for computing discrete cosine transform

Abstract

In this letter, an efficient algorithm for computing the discrete cosine transform (DCT) is presented. It is based on an index mapping which converts an odd-length DCT to a realvalued DFT of the same length using permutations and sign changes only. The real-valued DFT can then be computed by efficient real-valued FFT algorithms such as the prime factor algorithm. The algorithm is more efficient than an earlier one because no postmultiplications are required.