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 |  موضوع: كتاب Conceptual Digital Signal Processing with MATLAB الثلاثاء 11 مايو 2021, 3:06 am | |
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أحضرت لكم كتاب
Conceptual Digital Signal Processing with MATLAB
Signals and Communication Technology
Keonwook Kim
و المحتوى كما يلي :
Contents
1 Preliminary Digital Filter Design . 1
1.1 Discrete Time Signal . 1
1.2 Design the Digital Filters 3
1.3 Filter Architecture 9
1.4 Digital Filter Definitions and Requirements . 12
1.5 What We Need for Further (Optional) . 16
1.6 Problems 18
2 Frequency and Signals in Discrete Domain 21
2.1 Continuous Sinusoid Signals 21
2.2 Sampling 40
2.3 Signal Representation . 46
2.4 Frequency in Discrete Time Signal . 56
2.5 Problems 67
References . 69
3 Fourier Analysis 71
3.1 How We Can Find the Magnitude of the Specific Frequency? 71
3.2 Signal Property and Frequency Distribution . 81
3.3 Discrete-Time Fourier Transform (DTFT) 83
3.4 Discrete Fourier Transform (DFT) 89
3.5 Problems 117
References . 122
4 Filters in Time Domain . 123
4.1 Digital Filter Revisited 123
4.2 Filter Properties with LTI 124
4.3 FIR and IIR Filters . 129
4.4 Frequency Response 136
xi4.5 Simple Filter Design 142
4.6 Problems 199
References . 202
5 Z-Transform . 203
5.1 Definition and Usage . 203
5.2 Filter and Z-Transform 217
5.3 Intuitive Filter Design . 241
5.4 Relation with Fourier Analysis 262
5.5 Problems 263
References . 266
6 Filter Design . 267
6.1 Filter Specifications 268
6.2 FIR Filters . 275
6.3 IIR Filters . 395
6.4 Problems 494
References . 500
7 Implementation Matters 503
7.1 Number Representations . 504
7.2 Filter Implementation Components . 516
7.3 FIR Filter Implementations . 553
7.4 IIR Filter Implementations . 558
7.5 Frequency Domain Filter Realization 563
7.6 Problems 593
References . 594
8 Filters with MATLAB 595
8.1 Fundamental Filter Design Methods . 595
8.2 Advanced Filter Design Methods . 603
8.3 MATLAB Code Generation 637
References . 643
Appendix A: MATLAB Fundamentals . 645
Appendix B: MATLAB Symbolic Math Toolbox . 661
Index
Index
Symbols
( ), 1
[ ], 1
2’s complement, 504
, 1
A
Absolute summability, 236
Additivity, 51
Aliasing, 65, 489
Allpass filter, 384, 479
Alternation theorem, 344
App, 596
Arguments, 1
Arithmetic mean, 513
Auto-completion, 611
Autocorrelation, 461
Auto-listing, 611
Autoregressive (AR) model, 446
Autoregressive Moving Average (ARMA)
model, 447
B
Band Pass Filter (BPF), 186, 192
Band Pass Filter (BPF) - FIR type III, 329
Band Stop Filter (BSF), 186, 195
Bartlett window, 304
Base, 505
BIBO stability, 236
BIBO stability condition, 135
Bilinear transformation, 399, 413, 426, 444,
493
Binary number, 504
Bit-reversed order, 572, 577
Blackman window, 304
Block convolution, 577, 581
Bohman window, 304
Bounded Input and Bounded Output (BIBO)
stability, 135
Brick wall specification, 276
Butterworth IIR filter, 395
C
Canonic form, 559
Cascade connection, 526
Cauchy residue theorem, 540
Causality, 129, 149
Causal system, 129
Ceiling function, 517
Chebyshev approximation, 344
Chebyshev polynomial, 343
Chebyshev window, 304
Coefficient quantization, 521
Commutative law, 53
Complex and nonlinear-phase equiripple
design, 380
Complex Chebyshev approximation, 380
Compressed, 49
Conjugate transpose (Hermitian conjugate),
354
Constrained least square design, 376
Continuous frequency distriution, 83
Convolution sum, 12, 53, 123
Convolution sum in frequency domain, 138
Convolution sum to multiplication property,
228
Coupled form for SOS structure, 532
Cutoff frequency, 274
Cyclic frequency, 274
 Springer Nature Singapore Pte Ltd. 2021
K. Kim, Conceptual Digital Signal Processing with MATLAB,
Signals and Communication Technology,
https://doi.org/10.1007/978-981-15-2584-1
673D
Decibel unit, 268
Decimation-in-frequency FFT, 572
Decimation-in-time Fast Fourier transform
(FFT), 565
Delta function, 35
Denormalize, 507
DFT for non-periodic signal, 98
DFT length, 105
DFT length for convolution sum, 141
DFT method - filter design, 150
DFT method without truncation, 356
Differentiator, 337
Dirac delta function, 35
Direct form, 554
Direct form I, 558
Direct form II, 559
Discrete delta function, 87
Discrete Fourier Transform (DFT), 89
Discrete frequency x, 59, 273
Discrete-Time Fourier Transform (DTFT), 83
Discrimination factor, 438
Double precision, 509
DTFT method - filter design, 142
Duality, 141
Dual poles, 244
Dual poles with zeros, 252
E
Effective frequency, 65
Effective radian frequency, 62
Elliptic filter, 430
Elliptic rational function, 431
Energy, 54
Energy ratio between the main lobe and side
lobe, 279
Entirety-based processing, 579
Equivalent filter, 554
Euler formula, 24, 57, 66, 90
Even (odd) function, 27
Expanded, 49
Expected value, 513
Exponent, 505
F
Filter, 12
Filtering length, 5
Filter order, 274
Final value theorem, 212
Finite Impulse Response (FIR) filter, 130
FIR filter advantages, 275
FIR filter gain, 632
FIR filter transformations, 187
FIR realization structures, 553
First kind Chebyshev polynomial, 406, 416,
424
Fixed-point designer, 618
Fixed-point number, 511, 619
Fixed-point number computation, 511
Flat top weighted window, 304
Flipped transposed FIR filter, 554
Floating-point number, 505
Floor function, 512
Flow graph, 570, 577
Fourier transform, 32, 36
Fourier transform for discrete time signal, 136
Four types of FIR filter with zero group delay,
285
Fraction length, 619
Fraction number, 512
Frame-based processing, 579
Frequency, 2
Frequency aliasing, 493
Frequency discretization, 83
Frequency edge specifications, 274
Frequency inversion, 199
Frequency resolution, 102
Frequency response, 234
Frequency sampling design - type I, 353
Frequency sampling design - type II, 360
Frequency sampling method, 353
Frequency shift, 192, 199
Frequency shift - DFT, 114
Frequency shift - DTFT, 87
Frequency transformation in IIR filter, 477
Fundamental frequency, 81, 89
G
Gaussian window, 304
Geometric series, 205
Gibbs phenomenon, 276
Group delay, 284, 385
H
Halfpower frequency, 274
Hamming window, 304
Hann (Hanning) window, 304
High Pass Filter (HPF), 7, 186, 188
High Pass Filter (HPF) - FIR type IV, 334
Hilbert transform, 339
I
IEEE standard 754, 509
Ill-condition, 523, 556
674 IndexIIR filter method summary, 494
Impulse invariance, 500
Impulse response, 52, 228
Impulse train, 96
Infinite Impulse Response (IIR) filter, 133
Initial values, 232
Initial value theorem, 212
Invalid radian frequency, 62
Inverse Z-transform, 213
K
Kaiser window, 304, 312
Kronecker delta function, 46
Kuhn–Tucker conditions, 377
LL
∞-norm, 539
L1-norm, 537
L2-norm, 538
Lagrangian, 377
Laplace transform, 399, 411, 423
Leakage factor, 309
Least Significant Bit (LSB), 504
Least squared error frequency domain design—
discrete frequency sampling DFT, 364
Least squared error frequency domain design—
integral squared error approximation
criterion, 372
L’Hospital’s rule, 35
Limit cycle, 563
Linear and Time Invariant (LTI), 52, 124
Linear and time invariant system, 14
Linearity, 51
Linearity - DFT, 113
Linearity - DTFT, 87
Linear phase, 275, 284
Linear prediction filter, 461
Low Pass Filter (LPF), 142
LPF design method selection, 185
LPF design procedure, 187
M
Magnitude, 268
Magnitude inversion, 188, 197
Main lobe, 279
Main lobe width, 291, 305
Mantissa, 505
MATLAB coder, 638
Maxflat filter, 459
Maximum deviation, 271
Minimum 4-term Blackman-Harris window,
293
Minimum attenuation, 271
Minimum group delay, 390
Minimum phase filter, 443, 479
Minimum phase filter design, 382
Minimum phase system, 389
Modified Bartlett-Hann window, 293
Most Significant Bit (MSB), 504
Moving Average (MA) model, 446
Multiplication, 234
Multiplication for convolution sum, 137
Multiplication property, 137
Multi poles with zeros, 258
N
Negative frequency, 24
Normalized frequency, 273
Not-A-Number (NaN), 507
Nuttall-defined minimum 4-term
Blackman-Harris window, 304
Nyquist sampling rate, 45, 59
O
Object-oriented programming, 604
Orthogonality, 32, 71, 91
Overlap-add method, 584
Overlap-save method, 586
P
Parallel connection, 527
Parametric methods, 446
Parks-McClellan algorithm, 380
Parseval’s theorem, 143, 177, 236, 278, 319,
322, 327, 331, 334, 337, 372, 376
Parseval’s theorem - DFT, 115
Parseval’s theorem - DTFT, 88
Partial fraction, 216, 527
Partial fraction expansion, 540
Parzen window, 304
Passband frequency, 274
Passband magnitude, 271
Passband ripple, 269
Peak-to-peak ripple, 396
Period, 72
Periodicity in spectrum, 67
Phase delay, 395
Phasor, 28
Pole, 220
Pole-zero plot, 221
Polynomial long division, 214
Positive (negative) frequency, 67
Power, 56
Prefiltering, 473
Index 675Pre-scaling, 592
Primitive low pass filter, 4
Probability density function, 513
Prony, 461, 473
Pseudoinverse, 366
Q
QR solver, 471
Quantization, 511, 548
Quantization effect, 587
Quantization error sources, 548
R
Radian frequency, 22, 62
Ramp function, 47
Random process, 513
Random variable, 513
Real sequence - DFT, 114
Real signal property, 210
Real-time signal, 1
Rectangular window, 291
Recursive filter, 132
Reflecting, 49
Region of Convergence (ROC), 205
Relatioinship between DTFT and DFT, 94
Relatioinship between Z-transform, DTFT, and
DFT, 218
Relative peak side lobe amplitude, 291
Relative sidelobe attenuation, 309
Remes exchange algorithm, 345
Remes exchange algorithm (Parks and
McClellan), 342
Restrictions for linear phased FIR filters, 288,
291
Reversal operations, 554
Rounding, 512
Rule of thumb for pairing poles and zeros, 527
S
Sample-based processing, 579
Sampling, 40
Sampling frequency, 40
Sampling period, 41
Saturation addition, 518
Saturation arithmetic, 518
Scalability, 51
Scaling, 48
Second moment, 513
Second-Order Section (SOS), 526
Selective factor, 438
Sensitivity, 523
Shifting, 48
Shift pattern for DFT, 111
Shift property - DFT, 114
Signal periodicity, 83
Signal power, 513
Signal-to-Noise Ratio (SNR), 514
Signal types and pole locations, 225
Sign bit, 504
Signed fraction number, 511
Signed integer, 504
Significand, 505
Simulink, 595
Sinc function, 37
Single pole, 244
Single pole with zero, 247
Single precision, 509
Single quantization noise, 551
Single Sideband (SSB) output, 339
Speedup, 642
Stability, 275
Statistical signal processing, 447
Steiglitz-McBride algorithm, 468
Stopband, 398
Stopband attenuation, 271
Stopband frequency, 274
Substitution method, 134
Symmetricity for impulse response, 284
System object, 604
T
Taylor window, 304
Tense, 1
Three transformations, 263
Time delay - Z-transform, 231
Time invariance, 51
Time reversal - DFT, 116
Time reversal - DTFT, 88
Time shift, 25
Time shift - DFT, 113
Time shift - DTFT, 87
Toolbox, 595
Transfer function, 230, 236
Transformation procedure from LPF, 199
Transform capability, 230
Transposed direct, 554
Transposed direct form II, 559
Transposition, 554
Transversal, 553
Transversal structure, 553
676 IndexTriangular window, 304
Truncated impulse response from DTFT, 373
Truncated LPF, 182
Truncation, 512
Tukey (tapered cosine) window, 293
Type I, 285
Type I Chebyshev filter, 406
Type II, 285
Type II Chebyshev filter, 416
Type II FIR filter, 316
Type II HPF, 323
Type III, 285
Type III and type IV FIR filter, 334
Type III FIR filter, 328
Type IV, 285
Type IV FIR filter, 332
U
Unbiased estimation, 514
Underflow, 520
Unit of frequency, 21
Unit-step function, 47
Untrimmed LPF, 182
V
Vandermonde matrix, 354
Variance, 513
Visual spectral resolution, 108
W
Weight values, 4
White noise, 461
Wilkinson’s polynomial, 521
Window Designer from MATLAB, 309
Windowing methods, 291
Window shape, 8
Word length, 619
Y
Yule-walker method - approximated, 447
Z
Z, 204
Z domain transformation, 477
Zero, 221
Zero group delay FIR filter, 285
Zero padding, 102, 108
Zero reflection, 389
Z-transform, 203
Z-transform properties, 208
Z-transforms for fundamentals, 206
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