| Preface |
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xiv | |
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1 | (6) |
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Mathematical Representation of Signals |
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2 | (2) |
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Mathematical Representation of Systems |
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4 | (1) |
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5 | (1) |
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6 | (1) |
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7 | (29) |
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8 | (1) |
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Review of Sine and Cosine Functions |
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9 | (2) |
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11 | (4) |
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Relation of Frequency to Period |
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12 | (1) |
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Phase Shift and Time Shift |
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13 | (2) |
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Sampling and Plotting Sinusoids |
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15 | (2) |
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Complex Exponentials and Phasors |
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17 | (5) |
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Review of Complex Numbers |
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17 | (1) |
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Complex Exponential Signals |
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18 | (1) |
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The Rotating Phasor Interpretation |
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19 | (2) |
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21 | (1) |
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22 | (5) |
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Addition of Complex Numbers |
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23 | (1) |
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23 | (1) |
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Phasor Addition Rule: Example |
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24 | (1) |
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25 | (1) |
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Summary of the Phasor Addition Rule |
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26 | (1) |
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Physics of the Tuning Fork |
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27 | (2) |
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Equations from Laws of Physics |
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27 | (2) |
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General Solution to the Differential Equation |
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29 | (1) |
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29 | (1) |
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Time Signals: More Than Formulas |
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29 | (1) |
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30 | (1) |
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31 | (5) |
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36 | (35) |
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The Spectrum of a Sum of Sinusoids |
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36 | (3) |
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38 | (1) |
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Graphical Plot of the Spectrum |
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38 | (1) |
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39 | (4) |
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Multiplication of Sinusoids |
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39 | (1) |
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40 | (1) |
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41 | (2) |
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43 | (4) |
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44 | (1) |
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Example of a Nonperiodic Signal |
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45 | (2) |
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47 | (3) |
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48 | (1) |
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Fourier Series Derivation |
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48 | (2) |
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Spectrum of the Fourier Series |
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50 | (1) |
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Fourier Analysis of Periodic Signals |
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51 | (6) |
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52 | (1) |
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DC Value of a Square Wave |
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53 | (1) |
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Spectrum of a Square Wave |
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53 | (1) |
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Synthesis of a Square Wave |
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54 | (1) |
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55 | (1) |
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Synthesis of a Triangle Wave |
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56 | (1) |
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Convergence of Fourier Synthesis |
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57 | (1) |
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57 | (3) |
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59 | (1) |
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59 | (1) |
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Frequency Modulation: Chirp Signals |
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60 | (3) |
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Chirp or Linearly Swept Frequency |
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60 | (2) |
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A Closer Look at Instantaneous Frequency |
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62 | (1) |
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63 | (1) |
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64 | (7) |
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71 | (30) |
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71 | (8) |
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Sampling Sinusoidal Signals |
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73 | (2) |
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75 | (1) |
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Spectrum of a Discrete-Time Signal |
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76 | (1) |
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77 | (1) |
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78 | (1) |
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Spectrum View of Sampling and Reconstruction |
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79 | (5) |
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Spectrum of a Discrete-Time Signal Obtained by Sampling |
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79 | (1) |
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79 | (2) |
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Aliasing Due to Under-Sampling |
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81 | (1) |
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Folding Due to Under-Sampling |
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82 | (1) |
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Maximum Reconstructed Frequency |
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83 | (1) |
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84 | (4) |
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87 | (1) |
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Discrete-to-Continuous Conversion |
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88 | (5) |
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Interpolation with Pulses |
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88 | (1) |
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Zero-Order Hold Interpolation |
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89 | (1) |
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90 | (1) |
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Cubic Spline Interpolation |
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90 | (1) |
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Over-Sampling Aids Interpolation |
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91 | (1) |
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Ideal Bandlimited Interpolation |
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92 | (1) |
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93 | (1) |
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94 | (2) |
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96 | (5) |
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101 | (29) |
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102 | (1) |
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The Running-Average Filter |
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102 | (3) |
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105 | (6) |
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An Illustration of FIR Filtering |
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106 | (1) |
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The Unit Impulse Response |
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107 | (1) |
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107 | (1) |
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Unit Impulse Response Sequence |
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108 | (1) |
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109 | (1) |
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Convolution and FIR Filters |
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110 | (1) |
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Computing the Output of a Convolution |
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110 | (1) |
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111 | (1) |
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Implementation of FIR Filters |
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111 | (4) |
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111 | (1) |
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112 | (1) |
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112 | (1) |
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112 | (1) |
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113 | (1) |
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113 | (2) |
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Internal Hardware Details |
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115 | (1) |
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Linear Time-Invariant (LTI) Systems |
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115 | (3) |
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116 | (1) |
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117 | (1) |
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117 | (1) |
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Convolution and LTI Systems |
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118 | (4) |
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Derivation of the Convolution Sum |
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118 | (2) |
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Some Properties of LTI Systems |
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120 | (1) |
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Convolution as an Operator |
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121 | (1) |
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Commutative Property of Convolution |
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121 | (1) |
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Associative Property of Convolution |
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121 | (1) |
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122 | (2) |
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124 | (2) |
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126 | (1) |
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126 | (4) |
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Frequency Response of FIR Filters |
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130 | (33) |
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Sinusoidal Response of FIR Systems |
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130 | (2) |
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Superposition and the Frequency Response |
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132 | (3) |
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Steady-State and Transient Response |
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135 | (2) |
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Properties of the Frequency Response |
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137 | (2) |
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Relation to Impulse Response and Difference Equation |
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137 | (1) |
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138 | (1) |
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138 | (1) |
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Graphical Representation of the Frequency Response |
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139 | (4) |
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139 | (1) |
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140 | (2) |
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142 | (1) |
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143 | (2) |
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Running-Average Filtering |
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145 | (6) |
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Plotting the Frequency Response |
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146 | (2) |
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Cascade of Magnitude and Phase |
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148 | (1) |
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Experiment: Smoothing an Image |
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149 | (2) |
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Filtering Sampled Continuous-Time Signals |
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151 | (4) |
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Example: Lowpass Averager |
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152 | (2) |
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154 | (1) |
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155 | (2) |
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157 | (6) |
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163 | (33) |
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Definition of the z-Transform |
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164 | (1) |
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The z-Transform and Linear Systems |
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165 | (2) |
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The z-Transform of an FIR Filter |
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166 | (1) |
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Properties of the z-Transform |
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167 | (2) |
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The Superposition Property of the z-Transform |
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168 | (1) |
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The Time-Delay Property of the z-Transform |
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168 | (1) |
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A General z-Transform Formula |
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169 | (1) |
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The z-Transform as an Operator |
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169 | (2) |
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169 | (1) |
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170 | (1) |
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Operator Notation in Block Diagrams |
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170 | (1) |
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Convolution and the z-Transform |
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171 | (4) |
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173 | (1) |
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174 | (1) |
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175 | (1) |
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Relationship Between the z-Domain and the w-Domain |
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175 | (6) |
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The z-Plane and the Unit Circle |
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176 | (1) |
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The Zeros and Poles of H (z) |
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177 | (1) |
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Significance of the Zeros of H (z) |
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178 | (1) |
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179 | (1) |
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Graphical Relation Between z and w |
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180 | (1) |
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181 | (5) |
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The L-Point Running-Sum Filter |
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181 | (2) |
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A Complex Bandpass Filter |
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183 | (2) |
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A Bandpass Filter with Real Coefficients |
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185 | (1) |
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Practical Bandpass Filter Design |
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186 | (3) |
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Properties of Linear-Phase Filters |
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189 | (1) |
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The Linear-Phase Condition |
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189 | (1) |
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Locations of the Zeros of FIR Linear-Phase Systems |
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189 | (1) |
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190 | (1) |
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191 | (5) |
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196 | (49) |
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The General IIR Difference Equation |
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197 | (1) |
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198 | (6) |
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Linearity and Time Invariance of IIR Filters |
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199 | (1) |
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Impulse Response of a First-Order IIR System |
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200 | (1) |
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Response to Finite-Length Inputs |
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201 | (1) |
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Step Response of a First-Order Recursive System |
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202 | (2) |
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System Function of an IIR Filter |
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204 | (6) |
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The General First-Order Case |
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205 | (1) |
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The System Function and Block-Diagram Structures |
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206 | (1) |
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206 | (1) |
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207 | (1) |
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The Transposed Form Structure |
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208 | (1) |
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Relation to the Impulse Response |
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209 | (1) |
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209 | (1) |
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210 | (2) |
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Poles or Zeros at the Origin or Infinity |
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211 | (1) |
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Pole Locations and Stability |
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211 | (1) |
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Frequency Response of an IIR Filter |
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212 | (4) |
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Frequency Response using MATLAB |
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213 | (1) |
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Three-Dimensional Plot of a System Function |
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214 | (2) |
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216 | (1) |
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The Inverse z-Transform and Some Applications |
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216 | (4) |
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Revisiting the Step Response of a First-Order System |
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217 | (1) |
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A General Procedure for Inverse z-Transformation |
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218 | (2) |
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Steady-State Response and Stability |
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220 | (3) |
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223 | (8) |
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z-Transform of Second-Order Filters |
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223 | (1) |
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Structures for Second-Order IIR Systems |
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224 | (1) |
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225 | (1) |
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Impulse Response of a Second-Order IIR System |
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226 | (1) |
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227 | (1) |
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228 | (3) |
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Frequency Response of Second-Order IIR Filter |
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231 | (5) |
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Frequency Response via MATLAB |
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232 | (1) |
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232 | (1) |
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Three-Dimensional Plot of System Functions |
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233 | (3) |
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Example of an IIR Lowpass Filter |
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236 | (1) |
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237 | (1) |
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238 | (7) |
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Continuous-Time Signals and LTI Systems |
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245 | (40) |
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246 | (2) |
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Two-Sided Infinite-Length Signals |
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246 | (1) |
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247 | (1) |
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248 | (1) |
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248 | (6) |
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Sampling Property of the Impulse |
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250 | (2) |
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252 | (1) |
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252 | (1) |
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Derivative of the Unit Step |
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252 | (2) |
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254 | (1) |
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Some Basic Continuous-Time Systems |
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254 | (1) |
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255 | (1) |
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Analogous Discrete-Time Systems |
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255 | (1) |
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Linear Time-Invariant Systems |
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255 | (5) |
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256 | (1) |
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256 | (1) |
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257 | (2) |
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Properties of Convolution |
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259 | (1) |
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Impulse Responses of Basic LTI Systems |
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260 | (1) |
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260 | (1) |
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261 | (1) |
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261 | (1) |
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261 | (2) |
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Evaluating Convolution Integrals |
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263 | (7) |
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263 | (4) |
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Evaluation of Discrete Convolution |
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267 | (1) |
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268 | (1) |
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Very Narrow Square Pulse Input |
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269 | (1) |
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Discussion of Convolution Examples |
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270 | (1) |
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Properties of LTI Systems |
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270 | (6) |
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Cascade and Parallel Combinations |
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270 | (2) |
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Differentiation and Integration of Convolution |
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272 | (1) |
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273 | (3) |
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Using Convolution to Remove Multipath Distortion |
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276 | (2) |
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278 | (1) |
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279 | (6) |
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285 | (22) |
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The Frequency Response Function for LTI Systems |
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285 | (4) |
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Plotting the Frequency Response |
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287 | (1) |
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288 | (1) |
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Magnitude and Phase Changes |
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288 | (1) |
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Response to Real Sinusoidal Signals |
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289 | (6) |
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290 | (1) |
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290 | (3) |
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Response to a General Sum of Sinusoids |
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293 | (1) |
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294 | (1) |
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295 | (3) |
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295 | (1) |
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296 | (1) |
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297 | (1) |
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297 | (1) |
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Application of Ideal Filters |
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298 | (2) |
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Time-Domain or Frequency-Domain? |
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300 | (1) |
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301 | (1) |
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302 | (5) |
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Continuous-Time Fourier Transform |
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307 | (39) |
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Definition of the Fourier Transform |
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308 | (2) |
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Fourier Transform and the Spectrum |
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310 | (2) |
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Limit of the Fourier Series |
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310 | (2) |
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Existence and Convergence of the Fourier Transform |
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312 | (1) |
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Examples of Fourier Transform Pairs |
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313 | (9) |
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Right-Sided Real Exponential Signals |
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313 | (1) |
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314 | (1) |
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Rectangular Pulse Signals |
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314 | (2) |
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316 | (1) |
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Impulse in Time or Frequency |
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317 | (1) |
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318 | (1) |
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319 | (3) |
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Properties of Fourier Transform Pairs |
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322 | (4) |
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322 | (2) |
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Symmetry Properties of Fourier Transform Pairs |
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324 | (2) |
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326 | (6) |
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326 | (1) |
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Fourier Transform of a Convolution |
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327 | (1) |
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Examples of the Use of the Convolution Property |
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328 | (1) |
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Convolution of Two Bandlimited Functions |
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328 | (1) |
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Product of Two Sinc Functions |
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329 | (1) |
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Partial Fraction Expansions |
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330 | (2) |
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332 | (3) |
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332 | (1) |
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333 | (1) |
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Systems Described by Differential Equations |
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334 | (1) |
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The Multiplication Property |
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335 | (2) |
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The General Signal Multiplication Property |
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335 | (1) |
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The Frequency Shifting Property |
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336 | (1) |
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Table of Fourier Transform Properties and Pairs |
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337 | (1) |
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Using the Fourier Transform for Multipath Analysis |
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337 | (4) |
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341 | (1) |
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342 | (4) |
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Filtering, Modulation, and Sampling |
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346 | (43) |
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Linear Time-Invariant Systems |
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346 | (12) |
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Cascade and Parallel Configurations |
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347 | (1) |
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348 | (3) |
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Frequency Selective Filters |
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351 | (1) |
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351 | (1) |
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Other Ideal Frequency Selective Filters |
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352 | (1) |
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Example of Filtering in the Frequency-Domain |
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353 | (2) |
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Compensation for the Effect of an LTI Filter |
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355 | (3) |
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Sinewave Amplitude Modulation |
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358 | (10) |
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Double-Sideband Amplitude Modulation |
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358 | (4) |
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DSBAM with Transmitted Carrier (DSBAM-TC) |
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362 | (4) |
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Frequency Division Multiplexing |
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366 | (2) |
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Sampling and Reconstruction |
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368 | (12) |
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The Sampling Theorem and Aliasing |
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368 | (2) |
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Bandlimited Signal Reconstruction |
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370 | (2) |
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Bandlimited Interpolation |
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372 | (1) |
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Ideal C-to-D and D-to-C Converters |
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373 | (2) |
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The Discrete-Time Fourier Transform |
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375 | (1) |
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376 | (1) |
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Discrete-Time Filtering of Continuous-Time Signals |
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377 | (3) |
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380 | (1) |
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381 | (8) |
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389 | (38) |
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390 | (1) |
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Too Many Fourier Transforms? |
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391 | (2) |
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Relation of the DTFT to the CTFT |
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392 | (1) |
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Relation of the DFT to the DTFT |
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393 | (1) |
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Relation of the DFT to the CTFT |
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393 | (1) |
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393 | (2) |
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Analysis of a Sum of Sinusoids |
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395 | (4) |
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DTFT of a Windowed Sinusoid |
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398 | (1) |
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Discrete Fourier Transform |
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399 | (6) |
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400 | (1) |
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Summary of the DFT Representation |
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401 | (1) |
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The Fast Fourier Transform (FFT) |
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402 | (1) |
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Negative Frequencies and the DFT |
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402 | (1) |
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403 | (2) |
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Spectrum Analysis of Finite-Length Signals |
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405 | (2) |
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Spectrum Analysis of Periodic Signals |
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407 | (1) |
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408 | (12) |
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409 | (1) |
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410 | (1) |
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Spectrogram of a Sampled Periodic Signal |
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410 | (1) |
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Resolution of the Spectrogram |
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411 | (1) |
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412 | (1) |
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Spectrogram of a Musical Scale |
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413 | (2) |
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Spectrogram of a Speech Signal |
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415 | (3) |
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418 | (2) |
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The Fast Fourier Transform (FFT) |
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420 | (3) |
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420 | (1) |
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421 | (2) |
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423 | (1) |
|
|
|
424 | (3) |
|
|
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427 | (16) |
|
|
|
428 | (1) |
|
Notation for Complex Numbers |
|
|
428 | (3) |
|
|
|
428 | (1) |
|
|
|
429 | (1) |
|
Conversion: Rectangular and Polar |
|
|
430 | (1) |
|
Difficulty in Second or Third Quadrant |
|
|
431 | (1) |
|
|
|
431 | (1) |
|
|
|
432 | (1) |
|
Algebraic Rules for Complex Numbers |
|
|
432 | (2) |
|
|
|
434 | (1) |
|
Geometric Views of Complex Operations |
|
|
434 | (4) |
|
Geometric View of Addition |
|
|
435 | (1) |
|
Geometric View of Subtraction |
|
|
436 | (1) |
|
Geometric View of Multiplication |
|
|
437 | (1) |
|
Geometric View of Division |
|
|
437 | (1) |
|
Geometric View of the Inverse, z-1 |
|
|
437 | (1) |
|
Geometric View of the Conjugate, z* |
|
|
438 | (1) |
|
|
|
438 | (3) |
|
|
|
439 | (1) |
|
Procedure for Finding Multiple Roots |
|
|
440 | (1) |
|
|
|
441 | (1) |
|
|
|
441 | (2) |
|
|
|
443 | (12) |
|
|
|
444 | (1) |
|
Matrix Operations and Variables |
|
|
444 | (2) |
|
|
|
445 | (1) |
|
Matrix and Array Operations |
|
|
445 | (1) |
|
A Review of Matrix Multiplication |
|
|
445 | (1) |
|
Pointwise Array Operations |
|
|
446 | (1) |
|
|
|
446 | (1) |
|
|
|
447 | (1) |
|
|
|
447 | (1) |
|
Printing and Saving Graphics |
|
|
447 | (1) |
|
|
|
447 | (1) |
|
MATLAB Built-in Functions |
|
|
448 | (1) |
|
|
|
448 | (1) |
|
|
|
448 | (1) |
|
Writing a MATLAB Function |
|
|
448 | (3) |
|
|
|
449 | (2) |
|
Debugging a MATLAB M-file |
|
|
451 | (1) |
|
|
|
451 | (4) |
|
|
|
452 | (1) |
|
Repeating Rows or Columns |
|
|
452 | (1) |
|
Vectorizing Logical Operations |
|
|
452 | (1) |
|
|
|
453 | (1) |
|
|
|
453 | (1) |
|
|
|
454 | (1) |
|
|
|
454 | (1) |
|
|
|
455 | (23) |
|
|
|
457 | (6) |
|
|
|
457 | (1) |
|
|
|
457 | (1) |
|
|
|
457 | (1) |
|
|
|
458 | (1) |
|
|
|
458 | (1) |
|
|
|
459 | (1) |
|
|
|
459 | (1) |
|
|
|
460 | (1) |
|
Laboratory: Manipulating Sinusoids with MATLAB |
|
|
460 | (1) |
|
|
|
461 | (1) |
|
|
|
461 | (1) |
|
|
|
461 | (2) |
|
Encoding and Decoding Touch-Tone Signals |
|
|
463 | (10) |
|
|
|
463 | (1) |
|
|
|
463 | (1) |
|
Background: Telephone Touch-Tone Dialing |
|
|
463 | (1) |
|
|
|
464 | (1) |
|
|
|
464 | (1) |
|
|
|
464 | (1) |
|
|
|
465 | (1) |
|
|
|
465 | (1) |
|
|
|
465 | (1) |
|
|
|
465 | (1) |
|
|
|
466 | (1) |
|
Simple Bandpass Filter Design |
|
|
467 | (1) |
|
|
|
468 | (1) |
|
Filter Bank Design: dtmfdesign.m |
|
|
468 | (1) |
|
A Scoring Function: dtmfscore.m |
|
|
469 | (1) |
|
DTMF Decode Function: dtmfrun.m |
|
|
470 | (1) |
|
|
|
471 | (1) |
|
|
|
471 | (1) |
|
|
|
472 | (1) |
|
|
|
473 | (5) |
|
|
|
473 | (1) |
|
|
|
473 | (1) |
|
Discrete-Time Convolution Demo |
|
|
473 | (1) |
|
Continuous-Time Convolution Demo |
|
|
474 | (1) |
|
|
|
475 | (1) |
|
Continuous-Time Convolution GUI |
|
|
475 | (1) |
|
|
|
475 | (1) |
|
|
|
475 | (1) |
|
Continuous-Time Convolution |
|
|
475 | (1) |
|
Continuous-Time Convolution Again |
|
|
476 | (1) |
|
Discrete-Time Convolution |
|
|
476 | (2) |
|
|
|
478 | (4) |
| Index |
|
482 | |