Preface |
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xiii | |
List of Figures |
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xv | |
1 Theory of Signals and Linear Systems |
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1 | (38) |
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1 | (1) |
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1 | (1) |
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1 | (1) |
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1.2.2 The Convolution Theorem |
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2 | (1) |
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1.3 Some Important Functions |
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2 | (8) |
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1.3.1 The Constant Function |
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2 | (1) |
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1.3.2 The Sine and the Cosine Functions |
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2 | (1) |
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1.3.3 The Heaviside Step Function |
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3 | (1) |
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4 | (2) |
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6 | (1) |
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1.3.6 Impulse Function or Dirac's Delta Function |
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7 | (2) |
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1.3.7 The Sampling Function |
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9 | (1) |
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1.3.8 Even and Odd Functions |
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9 | (1) |
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1.3.9 Some Elementary Properties of Functions |
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9 | (1) |
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1.4 Basic Fourier Analysis |
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10 | (7) |
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1.4.1 The Trigonometric Fourier Series |
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12 | (3) |
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1.4.2 The Compact Fourier Series |
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15 | (1) |
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1.4.3 The Exponential Fourier Series |
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15 | (2) |
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17 | (6) |
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1.5.1 Bilateral Exponential Signal |
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19 | (1) |
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1.5.2 Transform of the Gate Function |
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19 | (1) |
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1.5.3 Fourier Transform of the Impulse Function |
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20 | (1) |
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1.5.4 Transform of the Constant Function |
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21 | (1) |
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1.5.5 Fourier Transform of the Sine and Cosine Functions |
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22 | (1) |
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1.5.6 Fourier Transform of the Complex Exponential |
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23 | (1) |
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1.5.7 Fourier Transform of a Periodic Function |
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23 | (1) |
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1.6 Some Properties of the Fourier Transform |
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23 | (6) |
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1.6.1 Linearity of the Fourier Transform |
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23 | (1) |
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24 | (1) |
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1.6.3 Symmetry of the Fourier Transform |
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25 | (1) |
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26 | (1) |
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1.6.5 Frequency Domain Shift |
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26 | (1) |
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1.6.6 Differentiation in the Time Domain |
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26 | (1) |
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1.6.7 Integration in the Time Domain |
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27 | (1) |
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1.6.8 The Convolution Theorem in the Time Domain |
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28 | (1) |
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1.6.9 The Convolution Theorem in the Frequency Domain |
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29 | (1) |
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29 | (4) |
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33 | (1) |
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1.9 Average, Power, and Autocorrelation |
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33 | (6) |
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1.9.1 Time Autocorrelation of Signals |
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34 | (5) |
2 Random Signals and Noise |
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39 | (60) |
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2.1 The Theory of Sets, Functions, and Measure |
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39 | (6) |
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40 | (1) |
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40 | (2) |
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42 | (1) |
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42 | (1) |
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42 | (2) |
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44 | (1) |
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45 | (2) |
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2.2.1 Axiomatic Approach to Probability |
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45 | (1) |
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46 | (1) |
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47 | (6) |
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2.3.1 Mean Value of a Random Variable |
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48 | (1) |
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2.3.2 Moments of a Random Variable |
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48 | (1) |
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2.3.3 The Variance of a Random Variable |
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48 | (1) |
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2.3.4 The Characteristic Function of a Random Variable |
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49 | (1) |
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2.3.5 Some Important Random Variables |
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49 | (2) |
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2.3.6 Joint Random Variables |
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51 | (2) |
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53 | (21) |
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2.4.1 The Autocorrelation Function |
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53 | (1) |
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54 | (3) |
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2.4.3 Wide Sense Stationarity |
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57 | (1) |
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58 | (1) |
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2.4.5 Properties of the Autocorrelation |
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58 | (5) |
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2.4.6 The Power Spectral Density |
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63 | (6) |
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2.4.7 Properties of the Power Spectral Density |
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69 | (5) |
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74 | (8) |
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2.5.1 Expected Value of the Output Signal |
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75 | (1) |
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2.5.2 The Response of Linear Systems to Random Signals |
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75 | (5) |
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80 | (2) |
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2.6 Analysis of a Digital Signal |
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82 | (8) |
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2.6.1 Autocorrelation of a Digital Signal |
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83 | (2) |
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2.6.2 Power Spectral Density for the Digital Signal |
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85 | (4) |
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2.6.3 The Digital Signal Bandwidth |
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89 | (1) |
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90 | (9) |
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2.7.1 The Two-Level Quantizer |
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90 | (1) |
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2.7.2 Quantization Noise Spectrum for a Two-level Quantizer |
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90 | (3) |
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2.7.3 Response of a Squarer Circuit |
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93 | (1) |
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2.7.4 Response of a Non-Linear Amplifier |
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94 | (1) |
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2.7.5 Response of an Ideal Diode |
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95 | (4) |
3 Amplitude Modulation Theory |
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99 | (22) |
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99 | (1) |
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100 | (3) |
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3.3 Amplitude Modulation by Random Signals |
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103 | (4) |
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3.3.1 Power of an AM Carrier |
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105 | (1) |
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3.3.2 Power Spectral Density |
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105 | (2) |
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107 | (5) |
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3.4.1 Quadratic Modulator |
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107 | (2) |
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3.4.2 Synchronous Modulator |
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109 | (1) |
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110 | (1) |
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111 | (1) |
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3.5 Suppressed Carrier Amplitude Modulation |
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112 | (1) |
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3.6 Spectrum of the AM-SC Signal |
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112 | (3) |
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3.6.1 Power Spectral Density |
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113 | (1) |
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3.6.2 The AM-SC Modulator |
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113 | (2) |
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115 | (1) |
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3.8 Amplitude Demodulation |
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116 | (2) |
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3.9 Noise Performance of Amplitude Modulation |
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118 | (3) |
4 Quadrature Amplitude Modulation Theory |
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121 | (22) |
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4.1 Quadrature Modulation with Random Signals |
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121 | (3) |
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4.2 Single Sideband Modulation |
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124 | (7) |
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124 | (1) |
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4.2.2 Fourier Transform of 1/πt |
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125 | (1) |
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4.2.3 Properties of the Hilbert Transform |
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126 | (1) |
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4.2.4 Producing the SSB Signal |
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126 | (2) |
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4.2.5 Lower Sideband SSB with Random Signal |
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128 | (3) |
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131 | (2) |
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133 | (1) |
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4.5 Quadrature Amplitude Demodulation |
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134 | (1) |
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4.6 Performance Evaluation of SSB |
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135 | (1) |
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4.7 Digital Quadrature Modulation |
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136 | (7) |
5 Angle Modulation Theory |
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143 | (24) |
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143 | (1) |
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5.2 Angle Modulation with Stochastic Signals |
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143 | (15) |
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144 | (2) |
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5.2.2 Low Modulation Index |
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146 | (2) |
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5.2.3 Medium Modulation Index |
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148 | (3) |
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5.2.4 High Modulation Index |
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151 | (7) |
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5.3 Frequency and Phase Demodulation |
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158 | (4) |
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5.4 Performance Evaluation of Angle Modulation |
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162 | (2) |
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5.5 Angle Modulation with a Digital Signal |
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164 | (3) |
6 Digital Modulation Theory |
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167 | (38) |
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167 | (1) |
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167 | (11) |
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167 | (1) |
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6.2.2 Representation by Basis Functions |
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168 | (2) |
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6.2.3 Receiver Design and Sufficient Statistic |
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170 | (3) |
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6.2.4 Maximum Likelihood Decision |
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173 | (1) |
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6.2.5 Error Probability and the Union Bound |
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174 | (4) |
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6.3 Digital Modulation Schemes |
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178 | (5) |
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6.3.1 Pulse Amplitude Modulation |
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179 | (1) |
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180 | (1) |
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6.3.3 Quadrature Modulation |
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181 | (2) |
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183 | (1) |
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6.5 Offset Phase Modulation |
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183 | (1) |
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6.6 The Transmission Pulse |
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184 | (2) |
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6.7 Constant Envelope Modulation |
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186 | (1) |
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6.8 The Rotated Constellation |
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187 | (7) |
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6.8.1 The Modulation Diversity Technique |
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188 | (1) |
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6.8.2 Rotating the QPSK Constellation |
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189 | (3) |
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6.8.3 The Presence of Channel Estimation Errors |
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192 | (1) |
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192 | (2) |
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6.9 Orthogonal Frequency Division Multiplexing |
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194 | (11) |
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6.9.1 Description of OFDM |
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195 | (4) |
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199 | (1) |
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6.9.3 OFDM with Random Signals |
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200 | (1) |
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6.9.4 Quadrature Modulation with Random Signals |
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200 | (5) |
Appendix A: Fourier and Hilbert Transforms |
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205 | (10) |
Appendix B: Biography of the Author |
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215 | (6) |
Appendix C: Glossary |
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221 | (12) |
References |
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233 | (8) |
Index |
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241 | |