Low-cost unified architectures for the computation of discrete trigonometric transforms

New hardware-oriented matrix formulations and their corresponding VLSI architectures are proposed for both radix2-and radix-4 fast algorithms of a variety of discrete trigonometric transforms (DXTs), including discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), and discrete Hartley transform (DHT). All the DXTs have the same complex kernel operation consisting of products of diagonal matrices and band matrices with equally spaced nonzero diagonals. New linear arrays based on the systolic mapping of the common kernel operation are designed which lead to hardware-efficient architectures requiring much fewer processing elements compared to other recently proposed unified DXT architectures of the same throughput rate.