Lth-Band Digital Filters

Lth-Band Digital Filters

Ljiljana Milic (Mihajlo Pupin Institute, Servia)
DOI: 10.4018/978-1-60566-178-0.ch007
OnDemand PDF Download:
$37.50

Abstract

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 signal processing. The common characteristic of Lth-band lowpass filters is that the 6 dB (or 3 dB) cutoff angular frequency is located at p/L, and the transition band is approximately symmetric around this frequency. In time domain, the impulse response of an Lth-band digital filter has zero valued samples at the multiples of L samples counted away from the central sample to the right and left directions. Actually, an Lth-band filter has the zero crossings at the regular distance of L samples thus satisfying the so-called zero intersymbol interference property. Sometimes the Lthband filters are called the Nyquist filters. The important benefit in applying Lth band FIR and IIR filters is the efficient implementation, particularly in the case L = 2 when every second coefficient in the transfer function is zero valued. Due to the zero intersymbol interference property, the Lth-band filters are very important for digital communication transmission systems. Another application is the construction of Hilbert transformers, which are used to generate the analytical signals. The Lth-band filters are also used as prototypes in constructing critically sampled multichannel filter banks. They are very popular in the sampling rate alteration systems as well, where they are used as decimation and interpolation filters in single-stage and multistage systems. This chapter starts with the linear-phase Lth-band FIR filters. We introduce the main definitions and present by means of examples the efficient polyphase implementation of the Lth-band FIR filters. We discuss the properties of the separable (factorizable) linear-phase FIR filter transfer function, and construct the minimum-phase and the maximum-phase FIR transfer functions. In sequel, we present the design and efficient implementation of the halfband FIR filters (L = 2). The class of IIR Lth-band and halfband filters is presented next. Particular attention is addressed to the design and implementation of IIR halfband filters. Chapter concludes with several MATLAB exercises for self study.

Complete Chapter List

Search this Book:
Reset
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
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
$37.50
Appendix A
About the Author