IIR Filters to Sampling Rate Conversion

IIR Filters to Sampling Rate Conversion

Ljiljana Milic (Mihajlo Pupin Institute, Servia)
DOI: 10.4018/978-1-60566-178-0.ch005
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Abstract

Infinite impulse response (IIR) filters are used in applications where the computational efficiency is the highest priority. It is well known that an IIR filter transfer function is of a considerably lower order than the transfer function of an FIR equivalent. The drawbacks of an IIR filter are the nonlinear phase characteristic and sensitivity to quantization errors. In multirate applications, the computational requirements for FIR filters can be reduced by the sampling rate conversion factor as demonstrated in Chapter IV. However, such a degree of computation savings cannot be achieved in multirate implementations of IIR filters. This is due to the fact that every sample value computed in the recursive loop is needed for evaluating an output sample. Based on the polyphase decomposition, several techniques have been developed which improve the efficiency of IIR decimators and interpolators as will be shown later on in this chapter. In this chapter, we consider first the direct implementation structures for IIR decimators and interpolators. In the sequel, we demonstrate the computational requirements for direct form IIR decimators and interpolators. The polyphase decomposition of an IIR transfer function is explained with its application to decimation and interpolation. Then, we demonstrate an efficient IIR polyphase structure based on all-pass subfilters, which is applicable to a restricted class of decimators and interpolators. In this chapter, we discuss the application of the elliptic minimal Q factor (EMQF) filter transfer function in constructing high-performance decimators and interpolators. The chapter concludes with a selection of 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