1. Classification of Signals and Systems 1
1.1 Introduction 1
1.2 Classification of Signals 3
1.3 Singularity Functions 9
1.4 Amplitude and Phase Spectra 15
1.5 Classification of Systems 17
1.6 Simple Manipulations of Discrete-time Signals 21
1.7 Representations of Systems 23
1.8 Analog-to-Digital Conversion of Signals 28 Review Questions 37
2. Fourier Analysis of Periodic and Aperiodic Continuous-Time Signals and Systems 40
2.1 Introduction 40
2.2 Trigonometric Fourier Series 41
2.3 Complex or Exponential form of Fourier Series 52
2.4 Parseval’s Identity for Fourier Series 58
2.5 Power Spectrum of a Periodic Function 59
2.6 Fourier Transform 62
2.7 Properties of Fourier Transform 64
2.8 Fourier Transform of Some Important Signals 75
2.9 Fourier Transform of Power and Energy Signals 103 Review Questions 119
3. Applications of Laplace Transform to System Analysis 127
3.1 Introduction 127
3.2 Definition 128
3.3 Region of Convergence (ROC) 128
3.4 Laplace Transforms of Some Important Functions 129
3.5 Initial and Final Value Theorems 137
3.6 Convolution Integral 138
3.7 Table of Laplace Transforms 142
3.8 Partial Fraction Expansions 144
3.9 Network Transfer Function 146
3.10 s-plane Poles and Zeros 147
3.11 Laplace Transform of Periodic Functions 154
3.12 Application of Laplace Transformation in Analysing Networks 157 Review Questions 183
4. z-Transforms 193
4.1 Introduction 193
4.2 Definition of the z-transform 196
4.3 Properties of z-transform 203
4.4 Evaluation of the Inverse z-transform 213 Review Questions 228
5. Linear Time Invariant Systems 236
5.1 Introduction 236
5.2 Properties of a DSP System 238
5.3 Difference Equation and its Relationship with System Function, Impulse Response and Frequency Response 256
5.4 Frequency Response 260 Review Questions 272
6. Discrete and Fast Fourier Transforms 279
6.1 Introduction 279
6.2 Discrete Convolution 279
6.3 Discrete-Time Fourier Transform (DTFT) 305
6.4 Fast Fourier Transform (FFT) 319
6.5 Computing an Inverse DFT by Doing a Direct DFT 344
6.6 Composite-radix FFT 352
6.7 Fast (Sectioned) Convolution 368
6.8 Correlation 373 Review Questions 376
7. Finite Impulse Response (FIR) Filters 380
7.1 Introduction 380
7.2 Magnitude Response and Phase Response of Digital Filters 381
7.3 Frequency Response of Linear Phase FIR Filters 384
7.4 Design Techniques for FIR Filters 385
7.5 Design of Optimal Linear Phase FIR Filters 409 Review Questions 414
9. Realisation of Digital Linear Systems 453
9.1 Introduction 453
9.2 Basic Realisation Block Diagram and the Signal-flow Graph 453
9.3 Basic Structures for IIR Systems 455
9.4 Basic Structures for FIR Systems 482 Review Questions 489
10. Effects of Finite Word Length in Digital Filters 496
10.1 Introduction 496
10.2 Rounding and Truncation Errors 496
10.3 Quantisation Effects in Analog-to-Digital Conversion of Signals 499
10.4 Output Noise Power from a Digital System 502
10.5 Coefficient Quantisation Effects in Direct Form Realisation of IIR filters 505
10.6 Coefficient Quantisation in Direct Form Realisation of FIR Filters 508
10.7 Limit Cycle Oscillations 510
10.8 Product Quantisation 513
10.9 Scaling 518
10.10 Quantisation Errors in the Computation of DFT 519 Review Questions 521
11. Multirate Digital Signal Processing 523
11.1 Introduction 523
11.2 Sampling 524
11.3 Sampling Rate Conversion 525
11.4 Signal Flow Graphs 535
11.5 Filter Structures 539
11.6 Polyphase Decomposition 541
11.7 Digital Filter Design 551
11.8 Multistage Decimators and Interpolators 555
11.9 Digital Filter Banks 565
11.10 Two-channel Quadrature Mirror Filter Bank 572
11.11 Multilevel Filter Banks 578 Review Questions 581
12. Spectral Estimation 584
12.1 Introduction 584
12.2 Energy Density Spectrum 584
12.3 Estimation of the Autocorrelation and Power Spectrum of Random Signals 586
12.4 DFT in Spectral Estimation 591
12.5 Power Spectrum Estimation: Non-Parametric Methods 593
12.6 Power Spectrum Estimation: Parametric methods 606 Review Questions 628
13. Adaptive Filters 631
13.1 Introduction 631
13.2 Examples of Adaptive filtering 631
13.3 The Minimum Mean Square Error Criterion 643
13.4 The Widrow LMS Algorithm 645
13.5 Recursive Least Square Algorithm 647
13.6 The Forward–Backward Lattice Method 650
13.7 Gradient Adaptive Lattice Method 654 Review Questions 655
14. Applications of Digital Signal Processing 658
14.1 Introduction 658
14.2 Voice Processing 658
14.3 Applications to Radar 671
14.4 Applications to Image Processing 673
14.5 Introduction to Wavelets 675 Review Questions 686
15. MATLAB Programs 688
15.1 Introduction 688
15.2 Representation of Basic Signals 688
15.3 Discrete Convolution 691
15.4 Discrete Correlation 693
15.5 Stability Test 695
15.6 Sampling Theorem 696
15.7 Fast Fourier Transform 699
15.8 Butterworth Analog Filters 700
15.9 Chebyshev Type-1 Analog Filters 706
15.10 Chebyshev Type-2 Analog Filters 712
15.11 Butterworth Digital IIR Filters 718
15.12 Chebyshev Type-1 Digital Filters 724
15.13 Chebyshev Type-2 Digital Filters 729
15.14 FIR Filter Design Using Window Techniques 735
15.15 Upsampling a Sinusoidal Signal 750
15.16 Down Sampling a Sinusoidal Sequence 750
15.17 Decimator 751
15.18 Estimation of Power Spectral Density (PSD) 751
15.19 PSD Estimator 752
15.20 Periodogram Estimation 753
15.21 State-space Representation 753
15.22 Partial Fraction Decomposition 753
15.23 Inverse z-transform 754
15.24 Group Delay 754
15.25 Overlap-add Method 755
15.26 IIR Filter Design-impulse Invariant Method 756
15.27 IIR Filter Design-bilinear Transformation 756
15.28 Direct Realisation of IIR Digital Filters 756
15.29 Parallel Realisation of IIR Digital Filters 757
15.30 Cascade Realisation of Digital IIR Filters 757
15.31 Decimation by Polyphase Decomposition 758
15.32 Multiband FIR Filter Design 758
15.33 Analysis Filter Bank 759
15.34 Synthesis Filter Bank 759
15.35 Levinson-Durbin Algorithm 759
15.36 Wiener Equation’s Solution 760
15.37 Short-time Spectral Analysis 760
15.38 Cancellation of Echo produced on the Telephone—Base Band Channel 761
15.39 Cancellation of Echo Produced on the Telephone—Pass Band Channel 763 Review Questions 765
Table of Contents
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2000
Tata McGraw-Hill