8 - Finite Impulse Response Design Techniques for Linear Phase SAW Filters

Abstract

The Remez exchange algorithm is used as a computation tool for the design of finite impulse response linear phase digital filters. Given a desired frequency response specification, it furnishes a finite set of impulse response coefficients for the digital filter synthesis that yield an optimum approximation to the desired frequency response. This algorithm can be applied to lowpass finite impulse response(FIR) linear phase digital design as well as to a variety of bandpass filter responses, including (a) optimum single passband filters, (b) multiple passband filters, (c) bandstop filters, and (d) equalizer filters with non-symmetric amplitude response. While the lowpass filter design is not applicable to SAW filters, it transpires that the other bandpass filter types can be applied to SAW implementation. The frequency response of a digital filter is different from that obtained for a classical analog type in that the digital one repeats periodically at the multiples of the sampling frequency. FIR linear phase filters represent stable structures because their impulse response is finite, while their transfer function contains only zeros and no poles in the complex frequency domain. One optimization technique for designing such filters involves minimax criteria, whereby the maximum error in the frequency response of the filter is minimized. This technique is used in the Remez algorithm in minimizing the ripple of an equiripple Chebyshev amplitude response.