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Abstract-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 signallimage communications is proposed. This structure uses only half as many multipliers as the previous best known scheme [l]. 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. 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 d-dimensional structures are fully-pipelined and consist of only d 1-D transform arrays and shift registers.