An efficient prime-factor algorithm for the discrete cosine transform and its hardware implementations

The prime-factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). In this paper, we present a new prime-factor algorithm for the DCT. We also design a prime-factor algorithm for the discrete sine transform which is based on the prime-factor DCT algorithm. Hardware implementations for the prime-factor DCT are also studied. We are especially interested in the hardware designs which are suitable for the VLSI implementations. We will show three hardware designs for the prime-factor DCT, including a VLSI circuit fabricated directly according to the signal-ow graph, a linear systolic array, and a mesh-connected systolic array. These three designs show the trade-oo between cost and performance. The methodology, which deals with general (N 1 N 2)-point DCTs, where N 1 and N 2 are mutually prime, is illustrated by converting a 15-point DCT problem into a (3 5)-point 2-D DCT problem.