VLSI architectures for the discrete wavelet transform

A class of VLSI architectures based on linear systolic arrays, for computing the 1-D Discrete Wavelet Transform (DWT), is presented. The various architectures of this class differ only in the design of their routing networks, which could be systolic, semisystolic, or RAM-based. These architectures compute the Recursive Pyramid Algorithm, which is a reformulation of Mallat´s pyramid algorithm for the DWT. The DWT is computed in real time (running DWT), using just N_w(J-1) cells of storage, where N_w is the length of the filter and J is the number of octaves. They are ideally suited for single-chip implementation due to their practical I/O rate, small storage, and regularity. The N-point 1-D DWT is computed in 2N cycles. The period can be reduced to N cycles by using N_w extra MAC´s. Our architectures are shown to be optimal in both computation time and in area. A utilization of 100% is achieved for the linear array. Extensions of our architecture for computing the M-band DWT are discussed. Also, two architectures for computing the 2-D DWT (separable case) are discussed. One of these architectures, based on a combination of systolic and parallel filters, computes the N²-point 2-D DWT, in real time, in N²+N cycles, using 2NN_w cells of storage