Subexpression encoded extrapolated impulse response FIR filter with perfect residual compensation

Earlier research has shown that filter impulse responses are quasi-periodic and filter coefficients can be approximated by extrapolation techniques. In this paper, a discrete coefficient extrapolated impulse response filter is proposed. Residual compensation technique is introduced to perfectly realize the filter coefficients. Both the extrapolated filter coefficients and the residuals are subexpression encoded to minimize the filter complexity. Numerical example shows that the proposed technique achieves minimum number of adders in the synthesis of the filter when compared with any other existing techniques.