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Chapter Seven. Specialized Lowpass FIR Filters

Seven Specialized Lowpass FIR Filters

In this chapter we present two implementations used to build computationally efficient, linear phase, finite impulse response (FIR) filters. We discuss these special FIR filters now because their behavior will be easier to understand using the z-transform concepts introduced in the last chapter.

The first filter type presented is called frequency sampling filters. They are in that special class of linear phase finite impulse response (FIR) filters built with recursive structures (using feedback). The Section 7.1 material is a bit advanced for DSP beginners, but it deserves study for two reasons. First, these filters can be very efficient (minimized computational workload) for narrowband lowpass filtering applications; and second, understanding their operation and design reinforces much of the DSP theory covered in previous chapters.

Section 7.2 discusses interpolated lowpass FIR filters. These filters, implemented with nonrecursive structures (no feedback), cascade multiple FIR filters to reduce computational workload. Their implementation is an innovative approach where more than one unit time delay separates the multipliers in a traditional tapped delay line structure.

The common thread among these two filter types is they're lean mean filtering machines. They wring every last drop of computational efficiency from a guaranteed stable, linear phase filter. In many lowpass filtering applications these FIR filter types can attain greatly reduced computational workloads compared to the traditional Parks-McClellan–designed FIR filters discussed in Chapter 5.

 
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Chapter One. Discrete Sequences and Systems

Chapter Two. Periodic Sampling

Chapter Three. The Discrete Fourier Transform

Chapter Four. The Fast Fourier Transform

Chapter Five. Finite Impulse Response Filters

Chapter Six. Infinite Impulse Response Filters

Chapter Seven. Specialized Lowpass FIR Filters

Chapter Eight. Quadrature Signals

Chapter Nine. The Discrete Hilbert Transform

Chapter Ten. Sample Rate Conversion

Chapter Eleven. Signal Averaging

Chapter Twelve. Digital Data Formats and Their Effects

Chapter Thirteen. Digital Signal Processing Tricks

Appendix A. The Arithmetic of Complex Numbers

Appendix B. Closed Form of a Geometric Series

Appendix C. Time Reversal and the DFT

Appendix D. Mean, Variance, and Standard Deviation

Appendix E. Decibels (dB and dBm)

Appendix F. Digital Filter Terminology

Appendix G. Frequency Sampling Filter Derivations

Appendix H. Frequency Sampling Filter Design Tables

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Understanding Digital Signal Processing
Understanding Digital Signal Processing (2nd Edition)
ISBN: 0131089897
EAN: 2147483647
Year: 2004
Pages: 183
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