Preface......Page 6
Contents......Page 7
1 Sampling of Continuous Time Signals......Page 10
1.1 Sampling Operation for Continuous Time Signals......Page 11
1.1.1 Sampling Frequency......Page 13
1.1.2 Mathematical Characterization of the Sampling Operation......Page 14
1.2 Sampling Operation......Page 15
1.2.1 The Fourier Transform of the Product Signal......Page 16
1.3 How to Draw Fourier Transforms of Product Signal and Digital Signal......Page 20
1.3.1 Drawing the Fourier Transform of Digital Signal......Page 34
1.4 Aliasing (Spectral Overlapping)......Page 39
1.4.1 The Meaning of the Aliasing (Overlapping)......Page 42
1.4.2 Drawing the Frequency Response of Digital Signal in Case of Aliasing (Practical Method)......Page 48
1.5 Reconstruction of an Analog Signal from Its Samples......Page 54
1.5.1 Approximation of the Reconstruction Filter......Page 60
1.6 Discrete Time Processing of Continuous Time Signals......Page 64
1.7 Continuous Time Processing of Digital Signals......Page 70
1.8 Problems......Page 77
2 Multirate Signal Processing......Page 80
2.1 Sampling Rate Reduction by an Integer Factor (Downsampling, Compression)......Page 81
2.1.1 Fourier Transform of the Downsampled Signal......Page 84
2.1.2 How to Draw the Frequency Response of Downsampled Signal......Page 87
2.1.3 Aliasing in Downsampling......Page 89
2.1.4 Interpretation of the Downsampling in Terms of the Sampling Period......Page 92
2.1.5 Drawing the Fourier Transform of Downsampled Signal in Case of Aliasing (Practical Method)......Page 101
2.2.1 Upsampling (Expansion)......Page 106
2.2.2 Mathematical Formulization of Upsampling......Page 107
2.2.3 Frequency Domain Analysis of Upsampling......Page 108
2.2.4 Interpolation......Page 112
2.2.5 Mathematical Analysis of Interpolation......Page 116
2.2.6 Approximation of the Ideal Interpolation Filter......Page 120
2.2.7 Anti-aliasing Filter......Page 135
2.3 Practical Implementations of C/D and D/C Converters......Page 137
2.3.1 C/D Conversion......Page 138
2.3.2 Sample and Hold......Page 139
2.3.3 Quantization and Coding......Page 143
2.3.4 D/C Converter......Page 145
2.4 Problems......Page 148
3 Discrete Fourier Transform......Page 154
3.1 Manipulation of Digital Signals......Page 155
3.1.2 Shifting of Periodic Digital Signals......Page 158
3.1.3 Some Well Known Digital Signals......Page 165
3.2 Review of Signal Types......Page 167
3.3 Convolution of Periodic Digital Signals......Page 174
3.3.1 Alternative Method to Compute the Periodic Convolution......Page 175
3.4 Sampling of Fourier Transform......Page 179
3.5 Discrete Fourier Transform......Page 181
3.5.1 Aliasing in Time Domain......Page 191
3.5.2 Matrix Representation of DFT and Inverse DFT......Page 193
3.5.3 Properties of the Discrete Fourier Transform......Page 194
3.5.4 Circular Convolution......Page 197
3.6 Practical Calculation of the Linear Convolution......Page 207
3.6.1 Evaluation of Convolution Using Overlap-Add Method......Page 208
3.6.2 Overlap-Save Method......Page 213
3.7.2 Decimation in Time FFT Algorithm......Page 216
3.7.3 Decimation in Frequency FFT Algorithm......Page 226
3.8 Total Computation Amount of the FFT Algorithm......Page 234
3.9 Problems......Page 239
4.1 Review of Systems......Page 241
4.1.1 Z-Transform......Page 244
4.1.2 Laplace Transform......Page 247
4.2 Transformation Between Continuous and Discrete Time Systems......Page 248
4.2.1 Conversion of Transfer Functions of LTI Systems......Page 253
4.2.2 Forward Difference Transformation Method......Page 254
4.2.3 Bilinear Transformation......Page 256
4.3 Analogue Filter Design......Page 261
4.3.1 Ideal Filters......Page 262
4.3.2 Practical Analog Filter Design......Page 266
4.3.3.1 Butterworth Filter Design......Page 268
4.3.3.2 Chebyshev Filter Design......Page 273
4.3.3.3 Elliptic Filters......Page 278
4.3.3.4 Bessel Filters......Page 279
4.3.4 Analog Frequency Transformations......Page 280
4.4.1 Low Pass Filter Circuits......Page 281
4.4.2 Analog High-Pass Filter Circuit Design......Page 287
4.4.4 Analog Bandstop Active Filter Circuits......Page 290
4.5 Infinite Impulse Response (IIR) Digital Filter Design (Low Pass)......Page 291
4.5.1 Generalized Linear Phase Systems......Page 297
4.6 Finite Impulse Response (FIR) Digital Filter Design......Page 298
4.6.1.1 FIR Filter Design by Windowing......Page 299
4.6.1.2 FIR Filter Design by Frequency Sampling......Page 304
4.7 Problems......Page 305
Bibliography......Page 307
Index......Page 308