Discrete-signal analysis and design

DISCRETE-SIGNAL ANALYSIS AND DESIGN......Page 4
CONTENTS......Page 10
Preface......Page 14
Introduction......Page 16
1 First Principles......Page 24
Sequence Structure in the Time and Frequency Domains......Page 25
Two-Sided Time and Frequency......Page 28
Discrete Fourier Transform......Page 29
Inverse Discrete Fourier Transform......Page 33
Frequency and Time Scaling......Page 34
Number of Samples......Page 36
Complex Frequency-Domain Sequences......Page 37
x(n) Versus Time and X(k) Versus Frequency......Page 38
2 Sine, Cosine, and θ......Page 42
Time and Spectrum Transformations......Page 44
Example 2-1: Nonlinear Amplifier Distortion and Square Law Modulator......Page 50
Example 2-2: Analysis of the Ramp Function......Page 54
Spectral Leakage. Noninteger Values of Time x(n) and Frequency X(k)......Page 58
Aliasing in the Frequency Domain......Page 63
Example 3-2: Analysis of Frequency-Domain Aliasing......Page 70
Aliasing in the Time Domain......Page 74
Smoothing the Rectangular Window, Without Noise and with Noise......Page 76
5 Multiplication and Convolution......Page 92
Polynomial Multiplication......Page 93
Convolution......Page 96
Discrete Convolution Basic Equation......Page 100
DFT and IDFT of Discrete Convolution......Page 104
Deconvolution......Page 109
6 Probability and Correlation......Page 110
Expected Value of x(n)......Page 111
Average Power of Noiseless Sequence......Page 114
Variance......Page 116
Gaussian (Normal) Distribution......Page 117
Cumulative Distribution......Page 118
Autocorrelation......Page 119
Cross-Correlation......Page 121
Autocovariance......Page 123
Correlation Coefficient......Page 125
7 The Power Spectrum......Page 128
Finding the Power Spectrum......Page 129
Example 7-1: The Use of Eq. (7-2)......Page 131
Random Gaussian Noise Spectrum......Page 133
Measuring the Power Spectrum......Page 135
Wiener-Khintchine Theorem......Page 136
System Power Transfer......Page 137
Cross Power Spectrum......Page 138
Example of Calculating Phase Noise......Page 140
Example of a Hilbert Transform of an Almost-Square Wave......Page 144
Mathematics of the Hilbert Transform......Page 152
Analytic Signal......Page 153
Example 8-2: Construction of Analytic Signal......Page 154
Single-Sideband RF Signals......Page 157
SSB Design......Page 160
Phasing Method SSB Transmitter......Page 163
Phasing Method SSB Receiver......Page 164
Filter Method SSB Receiver......Page 165
Discrete Derivative......Page 168
State-Variable Solutions......Page 170
Using the Discrete Derivative to Solve a Time Domain Discrete Differential Equation......Page 174
Glossary......Page 178
Index......Page 186