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On the Design of Sparse Half-Band Like FIR Filters

In this work we consider the design of sparse FIR filters, i.e. filters with few non-zero multiplications. The considered filters have half-band like properties, but with slightly relaxed specifications compared with actual half-band filters. We propose a filter design technique where the number of non-zero filter coefficients is minimized. It is shown by examples that it is possible to take advantage of an increased passband ripple only to obtain a half-band like solution with fewer non-zero multiplications. Decreasing the passband edge only does not give such a direct improvement.