Optimal Unified Architectures for the Real-Time Computation of Time-Recursive Discrete Sinusoidal Transforms

Abstract

An optimal unified architecture that can efficiently compute the Discrete Cosine, Sine, Hartley, Fourier, Lapped Orthogonal, and the Complex Lapped transforms for a continuous input data stream is proposed. This structure uses only half as many multipliers as the previous best known scheme [1]. This architecture is regular, modular, and has only local interconnections in both the data and control paths. There is no limitation on the transform size N and only 2N - 2 multipliers are needed for the DCT. The throughput of this scheme is one input sample per clock cycle. We provide a theoretical justification by showing that any discrete transform whose basis functions satisfy the Fundamental Recurrence Formula has a second-order autoregressive structure in its filter realization. We also demonstrate that dual generation transform pairs share the same autoregressive structure. We extend these time-recursive concepts to multi-dimensional transforms. The resulting multi-dimensional structure are fully- pipelined and consist of only d 1-D transform arrays and shift registers, where d is the dimension.