Complementary Filter Pairs

Complementary Filter Pairs

Ljiljana Milic (Mihajlo Pupin Institute, Servia)
DOI: 10.4018/978-1-60566-178-0.ch008
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Abstract

Digital filters with complementary characteristics find many applications in practice. In this chapter, we concentrate on the properties and construction of complementary filters and filter pairs. An important application of complementary property is deriving a new transfer function from the existing one. A highpass filter can be obtained as a complement of the lowpass filter, and also a bandstop filter can be considered as a complement of the bandpass filter. Complementary lowpass/highpass and bandpass/bandstop filter pairs are popular because of very attractive implementations. Namely, the two complementary filters in the pair are implemented at the cost of a single one. Complementary filter pairs, usually lowpass/highpass filter pairs, are widely used whenever there is a need to split the signal into two adjacent subbands and reconstruct it after some processing performed in the subbands. They are used as basic building blocks in constructing analysis and synthesis multichannel filter banks. Moreover, the complementary filter pairs are used in constructing low sensitivity complex filtering structures. In some applications, such as signal analysis, the complementary filter pairs are used to separate a signal into two bands, and the filtered signals are processed without need to reconstruct it. Another application is digital audio where the signal is separated into two (three) bands resulting in the signals that are feed inside two (three) loudspeakers. In this chapter, at the beginning we introduce the basic definitions of the complementary properties that will be used through the chapter. We use then the complementary properties to construct FIR and IIR highpass filters from the existing lowpass filters. In the sequel, we consider the analysis and synthesis filter pairs. We present the design and efficient implementations of FIR and IIR complementary filter pairs. Chapter concludes with MATLAB Exercises for 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