Theoretical analysis for recursive computation of discrete sinusoidal transforms

The theoretical basis for the optimal unified architecture that can efficiently compute the discrete cosine, sine, Hartley, Fourier, lapped orthogonal, and complex lapped transforms for a continuous input data stream is proposed. It is shown 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. Moreover, it is optimal in the sense that the number of the multipliers used is minimum and both speed and area are asymptotically optimal