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Digital Filters: Third Edition

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Digital Filters: Third Edition Cover

ISBN13: 9780486650883
ISBN10: 048665088x
All Product Details

 

Synopses & Reviews

Publisher Comments:

This introductory text examines digital filtering — the processes of refining signals
— and its relevance to many applications, particularly computer-related functions. Assuming only a knowledge of calculus and some statistics, it concentrates on linear signal processing, with some consideration of roundoff effects and Kalman filters. Numerous examples and exercises.

Synopsis:

Introductory text examines role of digital filtering in many applications, particularly computers. Focus on linear signal processing; some consideration of roundoff effects, Kalman filters. Only calculus, some statistics required.

About the Author

Richard W. Hamming: The Computer Icon

Richard W. Hamming (1915-1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004.

In the Author's Own Words:

"The purpose of computing is insight, not numbers."

"There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think."

"Whereas Newton could say, 'If I have seen a little farther than others, it is because I have stood on the shoulders of giants, I am forced to say, 'Today we stand on each other's feet.' Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way."

"If you don't work on important problems, it's not likely that you'll do important work." — Richard W. Hamming

Table of Contents

  Preface to the third edition

1. Introduction

  1.1 What is a digital filter?

  1.2 Why should we care about digital filters?

  1.3 How shall we treat the subject?

  1.4 General-purpose versus special-purpose computers

  1.5 Assumed statistical background

  1.6 The distribution of a statistic

  1.7 Noise amplification in a filter

  1.8 Geometric progressions

2. The frequency approach

  2.1 Introduction

  2.2 Aliasing

  2.3 The idea of an eigenfunction

  2.4 Invariance under translation

  2.5 Linear systems

  2.6 The eigenfunctions of equally spaced sampling

  2.7 Summary

3. Some classical applications

  3.1 Introduction

  3.2 Least-squares fitting of polynomials

  3.3 Least-squares quadratics and quartics

  3.4 Modified least squares

  3.5 Differences and derivatives

  3.6 More on smoothing: decibles

  3.7 Missing data and interpolation

  3.8 A class of nonrecursive smoothing filters

  3.9 An example of how a filter works

  3.10 Integration: recursive filters

  3.11 Summary

4. Fourier series: continuous case

  4.1 Need for the theory

  4.2 Orthogonality

  4.3 Formal expansions

  4.4 Odd and even functions

  4.5 Fourier series and least squares

  4.6 Class of functions and rate of convergence

  4.7 Convergence at a point of continuity

  4.8 Convergence at a point of discontinuity

  4.9 The complex Fourier series

  4.10 The phase form of a Fourier series

5. Windows

  5.1 Introduction

  5.2 Generating new Fourier series: the convolution theorems

  5.3 The Gibbs phenomenon

  5.4 Lanczos smoothing: The sigma factors

  5.5 The Gibbs phenomenon again

  5.6 Modified Fourier series

  5.7 The von Hann window: the raised cosine window

  5.8 Hamming window: raised cosine with a platform

  5.9 Review of windows

6. Design of nonrecursive filters

  6.1 Introduction

  6.2 A low-pass filter design

  6.3 Continuous design methods: a review

  6.4 A differentiation filter

  6.5 Testing the differentiating filter on data

  6.6 New filters from old ones: sharpening a filter

  6.7 Bandpass differentiators

  6.8 Midpoint formulas

7. Smooth nonrecursive filters

  7.1 Objections to ripples in a transfer function

  7.2 Smooth filters

  7.3 Transforming to the Fourier series

  7.4 Polynomial Processing in general

  7.5 The design of a smooth filter

  7.6 Smooth bandpass filters

8. The Fourier integral and the sampling theorem

  8.1 Introduction

  8.2 Summary of results

  8.3 The Sampling theorem

  8.4 The Fourier integral

  8.5 Some transform pairs

  8.6 Band-limited functions and the Sampling theorem

  8.7 The convolution theorem

  8.8 The effect of a finite sample size

  8.9 Windows

  8.10 The uncertainty principle

9. Kaiser windows and optimization

  9.1 Windows

  9.2 Review of Gibbs Phenomenon and the Rectangular window

  9.3 The Kaiser window: I subscript 0-sinh window

  9.4 Derivation of the Kaiser formulas

  9.5 Design of a bandpass filter

  9.6 Review of Kaiser window filter design

  9.7 The same differentiator again

  9.8 A particular case of differentiation

  9.9 Optimizing a design

  9.10 A Crude method of optimizing

10. The finite Fourier series

  10.1 Introduction

  10.2 Orthogonality

  10.3 Relationship between the discrete and continuous expansions

  10.4 The fast Fourier transform

  10.5 Cosine expansions

  10.6 Another method of design

  10.7 Padding out zeros

11. The spectrum

  11.1 Review

  11.2 Finite sample effects

  11.3 Aliasing

  11.4 Computing the spectrum

  11.5 Nonharmonic frequencies

  11.6 Removal of the mean

  11.7 The phase spectrum

  11.8 Summary

12. Recursive filters

  12.1 Why recursive filters?

  12.2 Linear differential equation theory

  12.3 Linear difference equations

  12.4 Reduction to simpler form

  12.5 Stability and the Z transformation

  12.6 Butterworth Filters

  12.7 A simple case of butterworth filter design

  12.8 Removing the phase: two-way filters

13. Chebyshev approximation and Chebyshev filters

  13.1 Introduction

  13.2 Chebyshev polynomials

  13.3 The Chebyshev Criterion

  13.4 Chebyshev filters

  13.5 Chebyshev filters, type 1

  13.6 Chebyshev filters, type 2

  13.7 Elliptic filters

  13.8 Leveling an error curve

  13.9 A Chebyshev identity

  13.10 An example of the design of an integrator

  13.11 Phase-free recursive filters

  13.12 The transient

14. Miscellaneous

  14.1 Types of Filter Design

  14.2 Finite arithmetic effects

  14.3 Recursive versus nonrecursive filters

  14.4 Direct modeling

  14.5 Decimation

  14.6 Time-varying filters

  14.7 References

  Index

What Our Readers Are Saying

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Average customer rating based on 1 comment:

nimali, October 9, 2006 (view all comments by nimali)
This is an excellent book for who is studing about digital filters.It provides a nice guidence to the student. it explains lot of theories with simple mathematics.thats why i like this book very much.
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(4 of 7 readers found this comment helpful)

Product Details

ISBN:
9780486650883
Author:
Hamming, R. W.
Publisher:
Dover Publications
Author:
Hamming, Richard W.
Author:
Engineering
Location:
Mineola, N.Y.
Subject:
Engineering - Civil
Subject:
Engineering - General
Subject:
Electronics - Digital
Subject:
Electronics - Circuits - General
Subject:
Digital filters (mathematics)
Subject:
Civil
Subject:
Electricity-General Electronics
Copyright:
Edition Description:
Trade Paper
Series:
Dover Civil and Mechanical Engineering
Publication Date:
19970731
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
304
Dimensions:
8.5 x 5.38 in 0.71 lb

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Digital Filters: Third Edition New Trade Paper
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Product details 304 pages Dover Publications - English 9780486650883 Reviews:
"Synopsis" by ,
Introductory text examines role of digital filtering in many applications, particularly computers. Focus on linear signal processing; some consideration of roundoff effects, Kalman filters. Only calculus, some statistics required.
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