数字信号处理:(第2版)(英文版)

.2.3.1 classification of discrete-time systems 16
2.4 time-domain representations of lti systems 21
2.4.1 the linear convolution sum 21
2.4.2 interconnections of lti systems 23
2.4.3 stability condition of lti systems 25
2.4.4 causality condition of lti systems 26
2.4.5 causal and anticausal sequences 26
2.5 linear constant-coefficient difference equations 27
2.5.1 recursive solution of difference equations 27
2.5.2 classical solution of difference equations 28
2.5.3 zero-input response and zero-state response 30
2.5.4 the impulse response of causal lti systems 31
2.5.5 recursive solution of impulse responses 31
2.5.6 classification of lti discrete-time systems 33
problems 34
3 transform-domain analysis of discrete-time signals and systems 37
3.1 the z-transform 37
3.1.1 definition of the z-transform 37
3.1.2 a general shape of the region of convergence 37
3.1.3 uniqueness of the z-transform 40
3.2 relation between the rocs and sequence types 41
3.3 the z-transform of basic sequences 44
3.4 the inverse z-transform 45
3.4.1 contour integral method 45
3.4.2 partial fraction expansion method 48
3.4.3 long division method 50
3.4.4 power series expansion method 52
3.5 properties of the z-transform 53
3.6 the discrete-time fourier transform 60
3.6.1 definition of the discrete-time fourier transform 60
3.6.2 convergence criteria 62
3.6.3 properties of the discrete-time fourier transform 66
3.6.4 symmetry properties of the discrete-time fourier transform 68
3.7 transform-domain analysis of lti discrete-time systems 70
3.7.1 the frequency response of systems 71
3.7.2 the transfer function of lti systems 74
3.7.3 geometric evaluation of the frequency response 77
3.8 sampling of continuous-time signals 79
3.8.1 periodic sampling 79
3.8.2 reconstruction of bandlimited signals 83
3.9 relations of the z-transform to the laplace transform 85
problems 88
4 the discrete fourier transform 92
4.1 the discrete fourier series 92
4.2 properties of the discrete fourier series 96
4.2.1 evaluation of the periodic convolution sum 99
4.3 the discrete fourier transform 100
4.4 properties of the discrete fourier transform 102
4.4.1 circular convolution theorems 107
4.5 linear convolutions evaluated by the circular convolution 109
4.6 linear time-invariant systems implemented by the dft 112
4.7 sampling and reconstruction in the z-domain 114
4.8 fourier analysis of continuous-time signals using the dft 117
4.8.1 fourier analysis of nonperiodic continuous-time signals 118
4.8.2 practical considerations 120
4.8.3 spectral analysis of sinusoidal signals 124
problems 126
5 fast fourier transform algorithms 130
5.1 direct computation and efficiency improvement of the dft 130
5.2 decimation-in-time fft algorithm with radix-2 131
5.2.1 butterfly-branch transmittance of the decimation-in-time fft 135
5.2.2 in-place computations 135
5.3 decimation-in-frequency fft algorithm with radix-2 137
5.4 computational method of the inverse fft 139
problems 139
6 digital filter structures 141
6.1 description of the digital filter structures 141
6.2 basic structures for iir digital filters 142
6.2.1 direct form i 142
6.2.2 direct form ii 143
6.2.3 cascade form 143
6.2.4 parallel form 145
6.3 basic structures for fir digital filters 147
6.3.1 direct forms 147
6.3.2 cascade forms 148
6.3.3 linear-phase forms 148
problems 150
7 design techniques of digital iir filters 152
7.1 preliminary considerations 152
7.1.1 frequency response of digital filters 154
7.2 discrete-time systems characterized by phase properties 156
7.3 allpass systems 158
7.3.1 nonminimum-phase systems represented by a cascade connection 160
7.3.2 group delay of the minimum-phase systems 161
7.3.3 energy delay of the minimum-phase systems 162
7.4 analog-to-digital filter transformations 163
7.4.1 impulse invariance transformation 164
7.4.2 step invariance transformation 167
7.4.3 bilinear transformation 170
7.5 design of analog prototype filters 175
7.5.1 analog butterworth lowpass filters 175
7.5.2 analog chebyshev lowpass filters 179
7.6 design of lowpass iir digital filters 184
7.6.1 design of lowpass digital filters using the impulse invariance 184
7.6.2 design of lowpass digital filters using the bilinear transformation 188
7.7 design of iir digital filters using analog frequency transformations 192
7.7.1 design of bandpass iir digital filters 192
7.7.2 design of bandstop iir digital filters 197
7.7.3 design of highpass iir digital filters 202
7.8 design of iir digital filters using digital frequency transformations 206
7.8.1 lowpass-to-lowpass transformation 207
7.8.2 lowpass-to-highpass transformation 209
7.8.3 lowpass-to-bandpass transformation 211
7.8.4 lowpass-to-bandstop transformation 214
problems 216
8 design of fir digital filters 217
8.1 properties of linear phase fir filters 217
8.1.1 the impulse response of linear-phase fir filters 218
8.1.2 the frequency response of linear-phase fir filters 220
8.1.3 characteristics of amplitude functions 222
8.1.4 constraints on zero locations 227
8.2 design of linear-phase fir filters using windows 228
8.2.1 basic techniques 228
8.2.2 window functions 230
8.2.3 design of linear-phase fir lowpass filters using windows 236
8.2.4 design of linear-phase fir bandpass filters using windows 239
8.2.5 design of linear-phase fir highpass filters using windows 241
8.2.6 design of linear-phase fir bandstop filters using windows 242
problems 244
9 finite-wordlength effects in digital signal processing 246
9.1 binary number representation with its quantization errors 246
9.1.1 fixed-point binary representation of numbers 246
9.1.2 floating-point representation 249
9.1.3 errors from truncation and rounding 249
9.1.4 statistical model of the quantization errors 253
9.2 analysis of the quantization errors in a/d conversion 254
9.2.1 statistical model of the quantization errors 254
9.2.2 transmission of the quantization noise through lti systems 257
9.3 coefficient quantization effects in digital filters 258
9.3.1 coefficient quantization effects in iir digital filters 258
9.3.2 statistical analysis of coefficient quantization effects 263
9.3.3 coefficient quantization effects in fir filters 266
9.4 round-off effects in digital filters 268
9.4.1 round-off effects in fixed-point realizations of iir filters 268
9.4.2 dynamic range scaling in fixed-point implementations of iir filters 274
9.5 limit-cycle oscillations in realizations of iir digital filters 278
9.5.1 zero-input limit cycle oscillations 278
9.5.2 limit cycles due to overflow 281
9.6 round-off errors in fft algorithms 288
9.6.1 round-off errors in the direct dft computation 288
9.6.2 round-off errors in fixed-point fft realization 289
problems 293
10 multirate digital signal processing 296
10.1 sampling rate changed by an integer factor 296
10.1.1 downsampling with an integer factor m 296
10.1.2 decimation by an integer factor m 299
10.1.3 upsampling with an integer factor l 302
10.1.4 interpolation by an integer factor l 303
10.2 sampling rate conversion by a rational factor 305
10.3 efficient structures for sampling rate conversion 307
10.3.1 equivalent cascade structures 308
10.3.2 polyphase decompositions 309
10.3.3 polyphase realization of decimation filters 310
10.3.4 polyphase realization of interpolation filters 311
problems 312
appendix a tables for the z-transform 315
appendix b table for properties of the discrete-time fourier transform 317
appendix c table for properties of the discrete fourier series 318
appendix d table for properties of the discrete fourier transform 319
appendix e table for the normalized butterworth lowpass filters 320
references 321