FIR Filters for Sampling Rate Conversion

The role of filters in sampling-rate conversion process has been discussed in Chapters II and III. Filters are used to suppress aliasing in decimators and to remove images in interpolators. The overall performance of a decimator or of an interpolator mainly depends on the characteristics of antialiasing and antiimaging filters. In Chapter III, we have considered the typical filter specifications and several methods for designing filter transfer functions that can meet the specifications. In this chapter, we are dealing with the implementation aspects of decimators and interpolators. The implementation problem arises from the unfavorable facts that filtering has to be performed on the side of the high-rate signal: in decimation filtering precedes the down-sampling, and in interpolation up-sampling precedes filtering. The goal is to construct a multirate implementation structure providing the arithmetic operations to be performed at the lower sampling rate. In this way, the overall workload in the sampling-rate conversion system can be decreased by the conversion factor M (L). The multirate filter implementation means that down-sampling or up-sampling operations are embedded into the filter structure. In this chapter, we are focused on the structures developed for finite impulse response (FIR) filters. The nonrecursive nature of FIR filters offers the opportunity to create implementation schemes that significantly improve the overall efficiency of FIR decimators and interpolators. This chapter concentrates on the direct implementation forms for decimators and interpolators and the implementation forms based on the polyphase decompositions. Memory saving solutions for polyphase decimators and interpolators are also presented. Finally, the efficiency of FIR polyphase decimators and interpolators is discussed. The chapter concludes with MATLAB exercises for the individual study.