Polynomial-Based Interpolation Filters—Part I: Filter Synthesis |
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Authors: | Jussi Vesma Tapio Saramaki |
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Affiliation: | (1) Nokia Corporation, Turku, FIN-20521, Finland;(2) Institute of Signal Processing, Tampere University of Technology, P.O. Box 553, FIN-33101, Tampere, Finland |
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Abstract: | This paper introduces a generalized design method for polynomial-based interpolation filters. These filters can be implemented
by using a modified Farrow structure, where the fixed finite impulse response (FIR) sub-filters possess either symmetrical
or anti-symmetrical impulse responses. In the proposed approach, the piecewise polynomial impulse response of the interpolation
filter is optimized directly in the frequency domain using either the minimax or least mean square criterion subject to the
given time domain constraints. The length of the impulse response and the degree of the approximating polynomial in polynomial
intervals can be arbitrarily selected. The optimization in the frequency domain makes the proposed design scheme more suitable
for various digital signal processing applications and enables one to synthesize interpolation filters for arbitrary desired
and weighting functions. Most importantly, the interpolation filters can be optimized in a manner similar to that of conventional
linear-phase FIR filters. |
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