Efficient formulation for the realization of discrete cosine transform using recursive structure

Abstract

Effective formulations for the conversion of the discrete Fourier transform (DFT) into a recursive structure are available and have been very effective for the realization using software, hardware and VLSI techniques. Little research work has been reported on the effective way to convert the discrete cosine transform (DCT) into a recursive form and the related realization. We propose a new method to convert a prime length DCT into a recursive structure. A trivial approach is to convert the DCT into the DFT and to apply Goertzel's (1958) algorithm for the rest of the realization. However, this method is inefficient. In our approach, we convert a prime length DCT into suitable transforms with half of the original length to effect fast realization. The number of operations is greatly reduced and the structure is extremely regular. >