Multi-Disciplinary Digital Signal Processing (eBook)

E.S. Gopi has authored six books, five of which have been published by Springer. He has also contributed 3 chapters to books published by Springer. He has several papers in international journals and conferences to his credit. He has 15 years of teaching and research experience. He is currently Assistant Professor, Department of Electronics and Communication Engineering, National Institute of Technology, Trichy, India and co-ordinator for Pattern recognition and computational intelligence laboratory. His research interests include  pattern recognition, digital signal processing and computational intelligence. The India International Friendship Society  (IIFS) has awarded him the “Shiksha Rattan Puraskar Award” for his meritorious services in the field of education. He was awarded  with the "Glory of India Gold Medal" by International Institute of Success Awareness. He was also awarded with "Best Citizens of India 2013" by The International Publishing House.

Acknowledgements 6
Contents 7
1 Sampling and Reconstruction of Signals 10
1.1 Sampling of Sinusoidal Signal 10
1.2 Fourier Series (FS) 20
1.2.1 Dirichlet Conditions 21
1.3 Fourier Transformation (FT) 21
1.4 Discrete Time Fourier Transformation (DTFT) and Sampling Theorem 22
1.5 Discrete Fourier Transformation (DFT) (Sampling the Frequency Domain) 27
1.5.1 Vector Space Interpretation of DFT 29
1.5.2 Fast Fourier Transformation 30
1.5.3 Sub-band Discrete Fourier Transformation 34
1.6 Continous System 36
1.7 Laplace Transformation (s-Transformation) 39
1.7.1 Properties of the ROC of the Laplace Transformation for the Right Sided Sequence 39
1.7.2 Inverse Laplace Transformation 40
1.8 Geometrical Interpretation of Computation of Magnitude Response of the Filter Using Pole-Zero Plot of s-Transformation 41
1.9 Discrete System 41
1.10 Z-Transformation 44
1.10.1 Properties of the ROC of the Z-Transformation for the Right-Sided Sequence 44
1.10.2 Inverse Z-Transformation 45
1.11 Response of the Digital Filter with the Typical Transfer Functionƒ 46
1.12 Geometrical Interpretation of Computation of Magnitude ƒ 49
2 Infinite Impulse Response (IIR) Filter 52
2.1 Impulse-Invariant Mapping 52
2.2 Bilinear Transformation Mapping 53
2.2.1 Frequency Pre-warping 54
2.2.2 Design of Digital IIR Filter using Butterworth Analog Filter and Impulse-Invariant Transformation 56
2.2.3 Design of Digital IIR Filter using Butterworth Analog Filter and Bilinear Transformation 56
2.2.4 Design of Digital IIR Filter Using Chebyshev Analog Filter and Impulse-Invariant Transformation 58
2.2.5 Design of Digital IIR Filter Using Chebyshev Analog Filter and Bilinear Transformation 58
2.2.6 Comments on Fig. 2.7 and Fig. 2.8 67
2.2.7 Design of High-Pass, Bandpass, and Band-Reject IIR Filter 68
2.3 Realization 81
2.3.1 Direct Form 1 81
2.3.2 Direct Form 2 81
2.3.3 Illustration 82
3 Finite Impulse Response Filter (FIR Filter) 86
3.1 Demonstration of Four Types of FIR Filter 87
3.2 Design of Linear Phase FIR Filter-Windowing Technique 99
3.2.1 Design of Low-Pass Filter 99
3.2.2 Design of High-Pass Filter 106
3.2.3 Design of Band Pass and Band Reject Filter 106
3.2.4 Windows Used to Circumvent Ripples in the Magnitude Response 114
3.3 FIR Filters that Have Identical Magnitude Response 122
4 Multirate Digital Signal Processing 129
4.1 Sampling Rate Conversion by the Factor MN 129
4.1.1 Upsampling (with N=1) 129
4.1.2 Downsampling (with M=1) 130
4.1.3 Comments on the Fig.4.1 131
4.2 Poly-phase Realization of the Filter for Interpolation 133
4.3 Poly-phase Realization of the Filter for Decimation 138
4.4 Quadrature Mirror Filter 145
4.5 Transmultiplexer 150
5 Statistical Signal Processing 155
5.1 Introduction to Random Process 155
5.1.1 Illustration on W.S.S.R.P and Nonstationary Random Process 155
5.2 Auto Regressive (AR), Moving average (MA) ƒ 158
5.2.1 Linear Prediction Model 159
5.3 Adaptive Filter 165
5.3.1 System Model 165
5.3.2 Filtering Noise 171
5.4 Spectral Estimation 174
5.4.1 Eigen Decomposition Method for Spectral Estimation 174
5.4.2 Pisarenko Harmonic Decomposition 176
5.4.3 MUSIC (Multiple Signal Classification) Method 177
5.4.4 ESPRIT (Estimation of Signal Parameters Via Rotational Invariance Technique) 178
6 Selected Applications in Multidisciplinary Domain 184
6.1 Multipath Transmission in Wireless Communication 184
6.2 Cyclic Prefix in Orthogonal Frequency Division Multiplexing (OFDM) 187
6.3 Projection Slice Theorem for Computed Tomography Imaging 189
6.4 Warped Discrete Fourier Transformation for Speech Signal 192
6.5 Nonuniform Discrete Fourier Transformation for the Compressive Sensing Applications 194
6.6 Nonuniform Sampling of Real Data in Multidisciplinary Applications-Linear Model for Regression 194
6.6.1 Maximum Likelihood Estimation 195
6.6.2 Least Square Estimation 196
6.6.3 Bayes Estimation 197
6.6.4 Kernel Smoothing Function for Regression 198
Appendix List of m-files 201
Index 204