كتاب Digital Signal Processing using MATLAB
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 كتاب Digital Signal Processing using MATLAB

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مُساهمةموضوع: كتاب Digital Signal Processing using MATLAB    كتاب Digital Signal Processing using MATLAB  Emptyالخميس 18 أغسطس 2022, 10:40 pm

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Digital Signal Processing using MATLAB
André Quinquis  

كتاب Digital Signal Processing using MATLAB  D_s_p_10
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Table of Contents
Preface . ix
Chapter 1. Introduction 1
1.1. Brief introduction to MATLAB . 1
1.1.1. MATLAB software presentation 1
1.1.2. Important MATLAB commands and functions 3
1.1.3. Operating modes and programming with MATLAB . 8
1.1.4. Example of work session with MATLAB . 10
1.1.5. MATLAB language 13
1.2. Solved exercises . 13
Chapter 2. Discrete-Time Signals 23
2.1. Theoretical background . 23
2.1.1. Mathematical model of 1D and 2D discrete-time signals 25
2.1.2. Basic 1D and 2D discrete-time signals . 26
2.1.3. Periodic 1D and 2D discrete-time signals representation
using the discrete-time Fourier series 26
2.1.4. Representation of non-periodic 1D and 2D discrete-time
signals by discrete-time Fourier transform . 27
2.1.5. Analytic signals . 27
2.2. Solved exercises . 29
2.3. Exercises . 51
Chapter 3. Discrete-Time Random Signals 55
3.1. Theoretical background . 55
3.1.1. Introduction . 55
3.1.2. Real random variables . 56
3.1.3. Random processes . 60vi Digital Signal Processing using MATLAB
3.2. Solved exercises . 64
3.3. Exercises . 80
Chapter 4. Statistical Tests and High Order Moments . 83
4.1. Theoretical background . 83
4.1.1. Moments . 84
4.1.2. Cumulants 84
4.1.3. Cumulant properties 85
4.1.4. Chi-square (Chi2) tests . 86
4.1.5. Normality test using the Henry line . 86
4.2. Solved exercises . 88
4.3. Exercises . 99
Chapter 5. Discrete Fourier Transform of Discrete-Time Signals 103
5.1. Theoretical background . 103
5.1.1. Discrete Fourier transform of 1D digital signals 104
5.1.2. DFT of 2D digital signals . 105
5.1.3. Z-transform of 1D digital signals 106
5.1.4. Z-transform of 2D digital signals 106
5.1.5. Methods and algorithms for the DFT calculation . 106
5.2. Solved exercises . 109
5.3. Exercises . 134
Chapter 6. Linear and Invariant Discrete-Time Systems 137
6.1. Theoretical background . 137
6.1.1. LTI response calculation 137
6.1.2. LTI response to basic signals . 139
6.2. Solved exercises . 141
6.3. Exercises . 169
Chapter 7. Infinite Impulse Response Filters . 173
7.1. Theoretical background . 173
7.1.1. Transfer function and filter specifications for infinite
impulse response (IIR) filters . 173
7.1.2. Design methods for IIR filters 174
7.1.3. Frequency transformations 180
7.2. Solved exercises . 182
7.3. Exercises . 194Preface vii
Chapter 8. Finite Impulse Response Filters 197
8.1. Theoretical background . 197
8.1.1. Transfer function and properties of FIR filters . 197
8.1.2. Design methods . 199
8.1.3. General conclusion about digital filter design . 203
8.2. Solved exercises . 204
8.3. Exercises . 213
Chapter 9. Detection and Estimation 215
9.1. Theoretical background . 215
9.1.1. Matched filtering: optimal detection of a known noisy signal 215
9.1.2. Linear optimal estimates 216
9.1.3. Least squares (LS) method 221
9.1.4. LS method with forgetting factor 222
9.2. Solved exercises . 223
9.3. Exercises . 239
Chapter 10. Power Spectrum Density Estimation 241
10.1. Theoretical background 241
10.1.1. Estimate properties 241
10.1.2. Power spectral density estimation . 242
10.1.3. Parametric spectral analysis . 245
10.1.4. Superresolution spectral analysis methods 250
10.1.5. Other spectral analysis methods 256
10.2. Solved exercises 257
10.3. Exercises . 277
Chapter 11. Time-Frequency Analysis . 279
11.1. Theoretical background 279
11.1.1. Fourier transform shortcomings: interpretation difficulties 279
11.1.2. Spectrogram 280
11.1.3. Time-scale analysis – wavelet transform . 281
11.1.4. Wigner-ville distribution . 284
11.1.5. Smoothed WVD (SWVD) 287
11.2. Solved exercises 288
11.3. Exercises . 304
Chapter 12. Parametrical Time-Frequency Methods 307
12.1. Theoretical background 307
12.1.1. Fractional Fourier transform . 307viii Digital Signal Processing using MATLAB
12.1.2. Phase polynomial analysis concept . 309
12.1.3. Time-frequency representations based on warping operators . 314
12.2. Solved exercises 317
12.3. Exercises . 338
Chapter 13. Supervised Statistical Classification . 343
13.1. Theoretical background 343
13.1.1. Introduction 343
13.1.2. Data analysis methods 344
13.1.3. Supervised classifiers . 348
13.2. Solved exercises 362
13.3. Exercises . 379
Chapter 14. Data Compression 383
14.1. Theoretical background 383
14.1.1. Transform-based compression methods 384
14.1.2. Parametric (predictive) model-based compression methods 385
14.1.3. Wavelet packet-based compression methods . 386
14.1.4. Vector quantization-based compression methods 387
14.1.5. Neural network-based compression methods . 388
14.2. Solved exercises 390
14.3. Exercises . 403
References . 405
Index .
Index
A
a posteriori probabilities 354
additive information measure 387
Akaike information criterion 248, 255
amplitude modulated 31, 32
analog filter design 174, 176, 188
analytic signal 27, 28, 286
anti-aliasing filter 33, 34
AR-2D model 385
Atlas-Marinovich distribution (AMD) 317
auto regressive (AR) model 246–249, 265,
266, 268, 277, 386
auto regressive moving average (ARMA)
model 245, 246, 277
autocorrelation matrix estimation 250
auto-terms 314
B
backpropagation algorithm 354
bandpass filter 78, 80, 165, 214, 238, 266,
282
bandstop filter 207
Bayes classifier 349, 354, 367, 368, 371,
375, 381
best basis 387
Bienaymé-Tchebycheff inequality 57
bilinear transformation method 179
binary information transmission 40
Blackman window 127, 205, 263, 269
Butterworth filters 34, 79
C
Capon’s method 257
Cauer filters 154
central limit theorem 70, 100
characteristic function 56, 57, 60, 83
Chebychev filters 176, 186, 189, 190, 191,
195, 224
chirp signal 39, 40, 234, 235, 288–290, 318,
319, 340
Chi-square (Chi2) test 86, 90, 92
clustering methods 387
Cohen class 315, 317
composed hypothesis 86
compression rate 383, 384, 387, 392, 395,
399, 403
constant-Q filtering 282
Cooley-Tukey algorithm 107
correlation coefficient 76, 77
correlogram 20, 241, 244
covariance matrix 62, 63, 219, 220, 345,
379, 384, 389
cross-terms 313, 314, 316, 324, 333, 340
cumulants 57, 83–85, 89, 96, 101
cumulative distribution function (cdf) 56,
60, 87
D
data analysis 5, 9, 344–346, 348
data compression 383–385, 387, 389
data overfitting 350
data redundancy 385, 386408 Digital Signal Processing using MATLAB
Daubechies wavelets 303
decimation-in-frequency 107
decimation-in-time 107
decision threshold 223–225
decomposition bases 386
decomposition tree 282
detection probability 227, 235, 239
digital filter design 174, 203
digital signal processing 1, 103
digital system modeling and simulation 1
discrete cosine transform (DCT) 105, 121,
125, 383, 384, 390, 392, 395–399, 403, 404
discrete Fourier transform (DFT) 27, 103–
108, 111–116, 119, 124–128, 131–134, 202,
242, 247, 383
discrete-time Fourier series (DTFS) 26, 47,
48
discrete-time Fourier transform (DTFT) 27,
28, 48, 49, 51, 52
discrete-time system 137
discriminant functions 349, 350, 354, 368
discriminant information 344
E
empirical mean error probability 349, 350
ergodicity 60, 61, 73, 81, 220
ESPRIT algorithm 253, 272
estimate bias 257
estimate variance 76, 243, 244, 248, 258
eye diagram 225, 226
F
false alarm probability 227, 235, 239
fast Fourier transform (FFT) 126, 133, 243,
260, 280, 311, 328
feature extraction 348
feature space 345
feature vector 344, 345, 348
filter bank 80, 282
filter coefficients 212, 303
filter gain 215
filter order 186, 195, 205
filter specifications 173–175, 179, 203, 210,
237
final prediction error (FPE) criterion 248
finite impulse response (FIR) filters 100,
197–214
Fletcher and Powell method 175
Fourier transform (FT) 26, 27, 57, 62, 103,
104, 110, 124, 126, 131, 132, 243–245, 249,
257, 269, 271, 273, 274, 279–282, 285, 310
fractional Fourier transform (FRFT) 307,
308, 317–320, 338
frequency sampling method 199, 202, 203,
206, 207, 214
frequency transformations 180, 181
fuzzification 352, 353
fuzzy KNN 351, 352, 367, 369, 371
fuzzy perceptron 356, 357, 359, 375, 376,
379
G
Gabor transform 281
Gaussian classes 356, 362, 366, 367
Gaussian distribution 64
Gaussian random process 63, 73
generalization capability 350, 362, 371, 380,
384
Gibbs phenomenon 200, 212
H
Haar wavelet 300, 303
Hamming window 131, 207, 271
Hanning window 132
Hebb and anti-Hebb rules 354, 389
Heisenberg-Gabor uncertainty principle 280
Henry line 86, 87, 89, 90, 101
high order ambiguity function (HAF) 309,
311, 312, 322, 324–330, 339, 340
high order instantaneous moment (HIM)
310–313
high order statistics 84, 85, 93
highpass filter 180, 206, 214
Hilbert transform (HT) 28, 29, 49–51, 199,
214
hyperbolic TFR class 316
I
image compression 383, 385, 390
impulse invariance method 176–178Index 409
independent random variables 67
indicial response 139, 154, 165, 166, 169,
183
infinite impulse response (IIR) filters 173,
174, 197, 203
instantaneous frequency 39, 286–288, 305,
315, 318, 319, 321–325, 327, 331, 338, 339,
341
interference terms 286, 287, 295, 304, 307
J, K
JADE algorithm 97
Kalman filter 218–220, 232, 233, 240
Karhunen-Loève transform (KLT) 345, 384,
385, 388, 389, 392, 395, 401, 403
kernel functions 361
K-means algorithm 387, 390, 399, 401
KNN (K nearest neighbor) classifiers 351–
353, 367, 369, 371, 381
kurtosis 85
L
Lagrange multipliers 360
learning techniques 343
learning vector quantization (LVQ) 354
least squares (LS) method 203, 207, 214,
221, 222
Leonov-Shiryayev relationship 84
Levinson-Durbin algorithm 247
linear convolution 138, 144, 145, 148, 249
linear discriminant analysis (LDA) 346,
347, 362, 365, 366, 380
linear time-invariant system (LTI) 137, 139,
140, 141, 150, 151, 159, 162, 165–167, 169,
245
linearly separable classes 348, 356
Lorentz’s equations 44
lowpass filter 75, 164, 174, 180, 182, 186,
188, 194, 204, 210–214
M
matched filter 215, 216, 223–225, 234, 235
MATLAB commands 3, 35
MATLAB functions 2, 9, 213, 258
MATLAB software 1, 2
MATLAB toolbox 376
matrix eigenanalysis 270, 275
matrix eigenvalues 6, 255
matrix eigenvectors 252, 384, 385
matrix operations 12
mean square error 345, 346, 354, 383, 385,
388, 390, 391, 394, 395, 401
membership coefficients 351–353, 357, 358
minimal entropy criterion 386
minimum description length (MDL)
criterion 256
mirror filters 282
model order estimation 247, 248
modified periodogram 243, 244, 258, 260,
261, 263, 264, 277
Morlet wavelet 292, 294
mother wavelet 281
moving average (MA) model 246, 248, 249
multi-component PPS (mc-PPS) 309, 312
multi-lags HAF (ml-HAF) 312, 326–328,
330, 339, 340
multilayer perceptron 354, 355, 371, 372,
374, 375
multiresolution analysis 281–284, 300, 302,
303, 386
MUSIC algorithm 251, 253, 257, 269, 271
N
neural KLT 388
neural networks 2, 348, 350, 353, 354, 388
Neyman-Pearson criterion 239
noise subspace 250, 252
non-linear frequency modulation 309
non-parametric estimation 351
non-stationary signals 280
normality test 86, 87
Nyquist theorem 177
O
Occam razor principle 350
optimal decision 223, 224, 226, 354
optimization methods 199, 203
orthonormal basis 384410 Digital Signal Processing using MATLAB
P
parametric estimation 350, 351
parametric spectral analysis 245, 277
Parseval theorem 104, 134
passband ripple 174, 194, 209, 237
pattern recognition 343, 344, 348
pattern signature 343
polynomial modeling 309, 323, 324, 330
polynomial phase signal (PPS) 309–313,
330, 339, 340
power spectral density (PSD) 41, 62, 63, 73,
76, 78, 81, 120, 121, 215, 218, 238, 240,
242, 243, 245–249, 253, 257, 258, 266–268,
271, 277, 278, 288
prewarping 315, 316
Prewitt filter 229
principal component analysis (PCA) 345,
346, 362–364, 366, 380
probability density function (pdf) 56–62,
64–70, 80, 81, 83–86, 88, 216, 349, 350
projection methods 345
Prony’s method 256
pulse modulation 40
R
Rader’s algorithm 108
radial basis function (RBF) 354, 361, 362
random vector 57, 58
receiver operating characteristics (ROC) 239
rectangular window 126, 131, 132, 200,
201, 205, 243
recursive least square (RLS) method 222,
229
Remez method 208, 209
Roberts filters 229
root-MUSIC algorithm 253
S
Sammon method 345, 347, 348, 380
Sammon stress 348
Schwarz inequality 59
self-organizing Kohonen map 389
separating hyperplane 356, 357, 359, 360
Shannon-Weaver entropy 386
short-time Fourier transform (STFT) 280–
282, 284
signal reconstruction 382
signal subspace 250, 252, 254–256, 271
signal-to-noise ratio (SNR) 20, 22, 64, 81,
269, 273, 274, 276, 328, 338, 339
skewness 85
smoothed WVD (SWVD) 287, 304
Sobel’s filters 227, 229
spectral aliasing 33, 285
spectral leakage 119, 133, 277
spectral resolution 118, 127–130, 132–134,
243–247, 250, 253, 257, 260, 263, 268, 269,
280, 282, 291, 292, 294
spectrogram 280, 282, 284, 288, 290–292,
305
stability 159, 176, 179
state-space model 219, 240
statistical classification 343, 344
statistical moments 58, 83
stochastic process 55, 56, 241
stopband attenuation 203, 205
strict sense stationarity (SSS) 60, 61
super-resolution spectral analysis 273, 250
supervised learning 343
support vector machines (SVM) 356, 359,
360–362, 375, 376, 379, 382
support vectors 359, 360, 379
T
time-frequency analysis 281, 290
time-frequency atoms 296, 304, 305
time-frequency plane 280, 282, 285, 287,
288, 292, 300, 307, 315
time-frequency representation (TFR) 96, 97,
290, 297, 305, 307, 309, 314–317, 331, 333,
334, 336, 340, 341
time-scale analysis 281
Toeplitz structure 63, 247
transfer function poles 151
transfer function sampling 175, 176
transfer function zeros 122, 151, 163, 170,
191, 194, 195, 218
transition band 33, 174, 200, 201, 203–205
triangular window 243Index 411
U, V
unwarping 316
vector quantization (VQ) 354, 387–389,
401, 403
W
warping operators 314, 315, 331, 334, 336,
337
wavelet family 281
wavelet packets 386
wavelet transform (WT) 281–283, 292, 295
Welch’s method 243, 244
wide sense stationarity (WSS) 61, 62
Wiener-Khintchine theorem 218, 245
Wigner-Ville distribution (WVD) 284, 285,
295–299, 305, 307, 331, 333, 340
windowg method 199, 200, 202, 204, 207
Winograd algorithm 108
Y, Z
Yule-Walker equations 246, 247, 249, 385
zero-padding 118, 134
zero-phase transfer function 197, 200, 202,
203
Z-transform (ZT) 103, 106, 121, 122

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