Optimal unified IIR architectures for 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 input data stream is proposed. This structure uses only half as many multipliers as the previous best known scheme. The proposed architecture is regular, modular, and locally connected. In the realisation of the discrete cosine transform, only 2N-2 multipliers are needed. A theoretical justification is provided showing that any discrete transform whose basic functions satisfy the fundamental recurrence formula has a second-order autoregressive structure in its filter realization. It is also demonstrated that dual generation transform pairs share the same autoregressive structure.<>