Digital Signal Processing

by Engelberg, Shlomo

• ISBN13: 9781848001183
• ISBN10: 1848001185
• Format: Hardcover
• Copyright: 2008-03-07
• Publisher: Springer Verlag

Summary

A mathematically rigorous but accessible treatment of digital signal processing that intertwines basic theoretical techniques with hands-on laboratory instruction is provided by this book. The book covers various aspects of the digital signal processing (DSP) "problem". It begins with the analysis of discrete-time signals and explains sampling and the use of the discrete and fast Fourier transforms. The second part of the book ” covering digital to analog and analog to digital conversion ” provides a practical interlude in the mathematical content before Part III lays out a careful development of the Z-transform and the design and analysis of digital filters.

Table of Contents

The Analysis of Discrete-time Signals
Understanding Sampling	p. 3
The Sample-and-hold Operation	p. 3
The Ideal Sampler in the Frequency Domain	p. 4
Representing the Ideal Sampler Using Complex Exponentials: A Simple Approach	p. 4
Representing the Ideal Sampler Using Complex Exponentials: A More Careful Approach	p. 5
The Action of the Ideal Sampler in the Frequency Domain	p. 9
Necessity of the Condition	p. 10
An Interesting Example	p. 11
Aliasing	p. 11
The Net Effect	p. 11
Undersampling	p. 14
The Experiment	p. 14
The Report	p. 15
Exercises	p. 15
Signal Reconstruction	p. 17
Reconstruction	p. 17
The Experiment	p. 18
The Report	p. 18
Exercises	p. 19
Time-limited Functions Are Not Band-limited	p. 21
A Condition for Analyticity	p. 21
Analyticity Implies Lack of Compact Support	p. 23
The Uncertainty Principle	p. 23
An Example	p. 24
The Best Function	p. 25
Exercises	p. 26
Fourier Analysis and the Discrete Fourier Transform	p. 29
An Introduction to the Discrete Fourier Transform	p. 29
Two Sample Calculations	p. 30
Some Properties of the DFT	p. 31
The Fast Fourier Transform	p. 35
A Hand Calculation	p. 36
Fast Convolution	p. 37
MATLAB, the DFT, and You	p. 37
Zero-padding and Calculating the Convolution	p. 39
Other Perspectives on Zero-padding	p. 41
MATLAB and the Serial Port	p. 42
The Experiment	p. 42
Exercises	p. 42
Windowing	p. 45
The Problems	p. 45
The Solutions	p. 47
Some Standard Window Functions	p. 47
The Rectangular Window	p. 48
The Triangular Window	p. 48
The Raised Cosine Window	p. 48
A Remark on Widths	p. 49
Applying a Window Function	p. 49
A Simple Comparison	p. 50
MATLAB's Window Visualization Tool	p. 51
The Experiment	p. 51
Exercises	p. 51
Signal Generation with the Help of MATLAB	p. 53
Introduction	p. 53
A Simple Sinewave Generator	p. 53
A Simple White Noise Generator	p. 54
The Experiment	p. 54
Exercises	p. 55
The Spectral Analysis of Random Signals	p. 57
The Problem	p. 57
The Solution	p. 58
Warm-up Experiment	p. 59
The Experiment	p. 61
Exercises	p. 63
Analog to Digital and Digital to Analog Converters
The General Structure of Sampled-data Systems	p. 67
Systems for Spectral Analysis	p. 67
Systems for Implementing Digital Filters	p. 68
The Operational Amplifier: An Overview	p. 69
Introduction	p. 69
The Unity-gain Buffer	p. 69
Why the Signal is Fed Back to V[subscript -]	p. 71
The "Golden Rules"	p. 71
The Inverting Amplifier	p. 72
Exercises	p. 72
A Simple Digital to Analog Converter	p. 75
The Digital to Analog Converter	p. 75
Practical Difficulties	p. 77
The Experiment	p. 78
Exercises	p. 79
The Binary Weighted DAC	p. 81
The General Theory	p. 81
Exercises	p. 83
The R-2R Ladder DAC	p. 85
Introduction	p. 85
The Derivation	p. 85
Exercises	p. 87
The Successive Approximation Analog to Digital Converter	p. 89
General Theory	p. 89
An Example	p. 90
The Sample-and-hold Subsystem	p. 91
The Single- and Dual-slope Analog to Digital Converters	p. 93
The Single-slope Converter	p. 93
Problems with the Single-slope A/D	p. 94
The Dual-slope A/D	p. 95
A Simple Example	p. 95
Exercises	p. 96
The Pipelined A/D	p. 99
Introduction	p. 99
The Fully Pipelined A/D	p. 100
The Experiment	p. 102
Exercises	p. 102
Resistor-chain Converters	p. 103
Properties of the Resistor Chain	p. 103
The Resistor-chain DAC	p. 103
The Flash A/D	p. 104
Exercises	p. 105
Sigma-Delta Converters	p. 109
Introduction	p. 109
The Sigma-Delta A/D	p. 110
Sigma-Delta A/Ds, Oversampling, and the Nyquist Criterion	p. 112
Sigma-Delta DACs	p. 113
The Experiment	p. 113
Digital Filters
Discrete-time Systems and the Z-transform	p. 117
The Definition of the Z-transform	p. 117
Properties of the Z-transform	p. 117
The Region of Convergence (ROC)	p. 117
Linearity	p. 119
Shifts	p. 119
Multiplication by k	p. 119
Sample Transforms	p. 120
The Transform of the Discrete-time Unit Step Function	p. 120
A Very Similar Transform	p. 120
The Z-transforms of Two Important Sequences	p. 121
A Two-sided Sequence	p. 122
Linear Time-invariant Systems	p. 122
The Impulse Response and the Transfer Function	p. 123
A Simple Example	p. 124
The Inverse Z-transform	p. 124
Inversion by Contour Integration	p. 124
Inversion by Partial Fractions Expansion	p. 125
Using MATLAB to Help	p. 126
Stability of Discrete-time Systems	p. 127
From Transfer Function to Recurrence Relation	p. 128
The Sinusoidal Steady-state Response of Discrete-time Systems	p. 130
MATLAB and Linear Time-invariant Systems	p. 132
Individual Commands	p. 132
The ltiview Command	p. 134
Exercises	p. 134
Filter Types	p. 139
Finite Impulse Response Filters	p. 139
Infinite Impulse Response Filters	p. 140
Exercises	p. 140
When to Use c (Rather than Assembly Language)	p. 143
Introduction	p. 143
A Simple Low-pass Filter	p. 143
A Comparison with an RC Filter	p. 144
The Experiment	p. 145
Exercises	p. 145
Two Simple FIR Filters	p. 147
Introduction	p. 147
The Experiment	p. 149
Exercises	p. 149
Very-narrow-band Filters	p. 151
A Very Simple Notch Filter	p. 151
From Simple Notch to Effective Bandpass	p. 151
The Transfer Function	p. 152
The Experiment	p. 152
Exercises	p. 153
Design of IIR Digital Filters: The Old-fashioned Way	p. 155
Analog Filter Design	p. 155
Two Simple Design Examples	p. 157
Why We Always Succeed in Our Attempts at Factoring	p. 159
The Bilinear Transform	p. 160
The Passage from Analog Filter to Digital Filter	p. 161
MATLAB and the Bilinear Transform	p. 162
The Experiment	p. 164
Exercises	p. 164
New Filters from Old	p. 165
Transforming Filters	p. 165
Functions that Take the Unit Circle into Itself	p. 165
Converting a Low-pass Filter into a High-pass Filter	p. 167
Changing the Cut-off Frequency of an Existing Low-pass Filter	p. 168
Going from a Low-pass Filter to a Bandpass Filter	p. 170
The Experiment	p. 171
The Report	p. 171
Exercises	p. 172
Implementing an IIR Digital Filter	p. 173
Introduction	p. 173
The Direct Form I Realization	p. 174
The Direct Form II Realization	p. 175
Trouble in Paradise	p. 175
The Solution: Biquads	p. 177
Exercises	p. 178
IIR Filter Design Using MATLAB	p. 181
Individual Commands	p. 181
The Experiment: Part I	p. 183
Fully Automatic Filter Design	p. 183
The Experiment: Part II	p. 183
Exercises	p. 184
Group Delay and Phase Delay in Filters	p. 185
Group and Phase Delay in Continuous-time Filters	p. 185
A Simple Example	p. 187
A MATLAB Experiment	p. 187
Group Delay in Discrete-time Systems	p. 188
Exercises	p. 189
Design of FIR Filters	p. 191
FIR Filter Design	p. 191
Symmetric FIR Filters	p. 194
A Comparison of FIR and IIR Filters	p. 197
The Experiment	p. 197
Exercises	p. 198
Implementing a Hilbert Filter	p. 199
An Introduction to the Hilbert Filter	p. 199
Problems and Solutions	p. 200
The Experiment	p. 200
Exercises	p. 201
The Goertzel Algorithm	p. 203
Introduction	p. 203
First-order Filters	p. 203
The DFT as the Output of a Filter	p. 204
Comparing the Two Methods	p. 205
The Experiment	p. 206
Exercises	p. 206
References	p. 207
Index	p. 209
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