Prime factor decomposition of the discrete cosine transform and its hardware realization
Paul P. N. Yang, Madihally J. Narasimha · 2005
The discrete cosine transform (DCT) is an useful tool in solving many digital signal processing problems. One of its more interesting applications is in the realization of a bandpass filter-bank that is necessary to perform conversion between time-division and frequency-division voice multiplexing systems. In this particular example the transform size is dictated by the sampling frequencies and the computationally-efficient power-of-2 algorithms may not applicable. To handle such situations, a new DCT algorithm based on a prime factor decomposition of the transform-length is presented in this paper. To begin with, the definition of the DCT is introduced with a brief discussion of the application mentioned. The existence of the prime factor decomposition technique is derived based on a similar decomposition for the discrete Fourier transform (DFT). The prime factor algorithm for the DCT (PFA-DCT) is then described step by step and followed by an example of a 12-point transform which delineates the method and brings out the essence of the algorithm. A hardware implementation of a 72-point DCT is outlined to illustrate the usefulness of this algorithm in practical systems.