FIR Filters for Sampling Rate Conversion

FIR Filters for Sampling Rate Conversion

Ljiljana Milic (Mihajlo Pupin Institute, Servia)
DOI: 10.4018/978-1-60566-178-0.ch004
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Abstract

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.

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Dedication
Table of Contents
Foreword
Miroslav D. Lutovac
Acknowledgment
Ljiljana Milic
Chapter 1
Ljiljana Milic
This chapter is a concise review of time-domain and transform-domain representations of single-rate discrete-time signals and systems. We consider... Sample PDF
Single-Rate Discrete-Time Signals and Systems: Background Review
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Chapter 2
Ljiljana Milic
Linear time-invariant systems operate at a single sampling rate i.e. the sampling rate is the same at the input and at the output of the system, and... Sample PDF
Basics to Multirate Systems
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Chapter 3
Ljiljana Milic
The role of filtering in sampling-rate conversion has been considered in Chapter II. The importance of filtering arises from the fact that the... Sample PDF
Filters in Multirate Systems
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Chapter 4
Ljiljana Milic
The role of filters in sampling-rate conversion process has been discussed in Chapters II and III. Filters are used to suppress aliasing in... Sample PDF
FIR Filters for Sampling Rate Conversion
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Chapter 5
Ljiljana Milic
Infinite impulse response (IIR) filters are used in applications where the computational efficiency is the highest priority. It is well known that... Sample PDF
IIR Filters to Sampling Rate Conversion
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Chapter 6
Ljiljana Milic
We have discussed so far the decimation and interpolation where the sampling rate conversion factor is an integer. However, the need for a... Sample PDF
Sampling Rate Converison by a Fractional Factor
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Chapter 7
Lth-Band Digital Filters  (pages 206-241)
Ljiljana Milic
Digital Lth-band FIR and IIR filters are the special classes of digital filters, which are of particular interest both in single-rate and multirate... Sample PDF
Lth-Band Digital Filters
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Chapter 8
Ljiljana Milic
Digital filters with complementary characteristics find many applications in practice. In this chapter, we concentrate on the properties and... Sample PDF
Complementary Filter Pairs
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Chapter 9
Ljiljana Milic
Digital filters with sharp transition bands are difficult, sometimes impossible, to be implemented using single-stage structures. A serious problem... Sample PDF
Multirate Techniques in Filter Design and Implementation
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Chapter 10
Ljiljana Milic
The initial concept of the frequency-response masking technique was introduced by Neuvo, Cheng-Yu and Mitra (1984). It was shown that the complexity... Sample PDF
Frequency-Reponse Masking Techniques
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Chapter 11
Ljiljana Milic
Comb filters are developed from the structures based on the moving average (boxcar) filter. The combbased filter has unity-valued coefficients and... Sample PDF
Comb-Based Filters for Sampling Rate Conversion
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Chapter 12
Ljiljana Milic
The purpose of this chapter is to illustrate by means of examples the construction of the analysis and synthesis filter banks with the use of FIR... Sample PDF
Examples of Multirate Filter Banks
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Appendix A
About the Author