Efficient recursive realization of FIR filters. I - The filter structures. II - Design and applications

The design of finite-impulse-response (FIR) filters comprising transversal block-delay sections followed by recursive sections and utilizing the time-domain response characteristic is reported. Recursive structures with piecewise-polynomial, piecewise-(polynomial/sinusoid), and piecewise-(polynomial/decaying sinusoid) impulse responses are developed and illustrated. The arithmetic required for such a filter is shown to be proportional to the number of piecewise sections rather than the filter length. Practical designs for high-pass and low-pass filters, narrowband filters, bandpass and bandstop filters, Hilbert transformers, and differentiators are realized using only a few piecewise sections. Response curves are provided, and a frequency-domain optimization scheme is presented.