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Optimized Design of Extrapolated Impulse Response FIR Filters with Raised-Cosine Windows

The impulse response of an FIR low-pass or high-pass filter has a quasi-periodic nature (Lim, 1990). As a result, extrapolated impulse response filters apply this similarity on side lobes to extend the length of the FIR filters and reduce the arithmetic complexity. In this paper, we select raised-cosine windows as the prototype for extrapolated function because they maintain distinct quasi-periodic characteristics in time domain. In order to improve the efficiency of extrapolation, we introduce complementary functions to approximate the envelope of the prototype, which is proved to be effective from examples in our work