Optimal unified architectures for the real-time computation of time-recursive discrete sinusoidal transforms

An optimal unified architecture that can efficiently compute the discrete cosine, sine, Hartley, Fourier, lapped orthogonal, and complex lapped transforms for a continuous stream of input data that arise in signal/image communications is proposed. This structure uses only half as many multipliers as the previous best known scheme (Liu and Chiu, 1993). The proposed architecture is regular, modular, and has only local interconnections in both 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. The authors 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. They also demonstrate that dual generation transform pairs share the same autoregressive structure. They extend these time-recursive concepts to multi-dimensional transforms. The resulting d-dimensional structures are fully-pipelined and consist of only d 1D transform arrays and shift registers