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

Abstract

Effective formulations for the conversion of the Discrete Fourier Transform (DFT) into recursive structure are available and have been found very effective for realization using software, hardware, and VLSI techniques. Little research work has been reported on an effective way to convert the Discrete Cosine Transform (DCT) into recursive form and the related realization. In this paper, we propose a new method to convert a prime length DCT into a recursive structure. A trivial approach is to use a conventional approach to convert the DCT into DFT and to apply Goertzel's algorithm for the rest of the realization. However, this method is inefficient and requires the realization of long length DFT's. In our approach, we suggest using some suitable mappings to convert a prime length DCT into two suitable transforms with approximately half of the original length to effect fast realization. The number of operations is greatly reduced and the structure is extremely regular.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>