Digital Signal Processing

Paperback | January 16, 2015

byTarun Kumar Rawat

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Digital Signal Processing is a comprehensive textbook designed for undergraduate and post-graduate students of engineering for a course on digital signal processing. Following the book's step-by-step approach, students can quickly master the fundamental concepts and applications of DSP. Eachtopic is explained lucidly through illustrations and solved examples. Divided into 17 Chapters, this text presents the introductory topics such as discrete-time signals and systems, sampling and quantization, convolution, discrete-time Fourier series, discrete-time Fourier transform, and z-transform in a rigorous fashion. Further, topics such as DFT, FFT, filterconcepts, filter structures, FIR filter design and IIR filter design are dealt in detail. It also covers the advanced topics such as finite word length effects, multirate DSP, optimum linear filters, and spectrum estimation techniques. The chapters are packed with numerous illustrations, solved examples, multiple choice questions, numerical exercises and MATLAB programs. Additional solved examples at the end of the book will provide some more practice to students.

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Digital Signal Processing is a comprehensive textbook designed for undergraduate and post-graduate students of engineering for a course on digital signal processing. Following the book's step-by-step approach, students can quickly master the fundamental concepts and applications of DSP. Eachtopic is explained lucidly through illustrati...

Tarun Kumar Rawat is Assistant Professor of division of Electronics and Communication Engineering at Netaji Subhas Institute of Technology (NSIT), New Delhi. He has completed his M. Tech. and PhD from the University of Delhi in the area of Signal Processing.
Format:PaperbackDimensions:1100 pages, 9.69 × 7.44 × 1.8 inPublished:January 16, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198081936

ISBN - 13:9780198081937


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Table of Contents

DedicationFeatures of the BookPrefaceBrief Content1. Discrete-Time Signals and Systems1.1 Introduction 11.2 Signals, Systems, and Signal Processing1.2.1 Basic Elements of a Digital Signal Processing Systems1.2.2 Advantages of Digital Signal Processing (DSP) over Analog Signal Processing (ASP)1.2.3 DSP Applications1.3 Classification of Signals1.3.1 Continuous-Time and Discrete-Time Signals1.3.2 Continuous-Valued and Discrete-Valued Signals 1.3.3 Multichannel andMultidimensional Signals1.3.4 Deterministic and RandomSignals1.4 Discrete-Time Signal or Sequence1.4.1 Finite-Length and Infinite-Length Signal 81.4.2 Right-Sided, Causal, Left-Sided, and Anticausal Signals1.5 Basic Operations on Discrete-Time Signals1.5.1 Signal Addition Operation1.5.2 Scalar Addition Operation1.5.3 SignalMultiplication Operation1.5.4 ScalarMultiplication Operation1.6 Transformations of the Independent Variable (Time)1.6.1 Time-Shifting1.6.2 Time-Scaling (Decimation and Interpolation1.6.3 Time-Reversal1.6.4 Combined Operations1.7 Some Basic Discrete-Time Signals1.7.1 Unit Step Signal1.7.2 Unit Impulse Signal (or Unit Sample Signal)1.7.3 Unit Ramp Signal 241.7.4 Discrete-Time Real Exponential Signal 251.7.5 Discrete-Time Sinusoidal Signal 261.7.6 Discrete-Time Complex Exponential Signal 271.8 Periodic and Aperiodic Signals 281.8.1 Properties of Periodic Signals 281.8.2 Periodicity of Discrete-Time Sinusoidal Signals 311.9 Energy and Power Signals 411.10 Even and Odd Signals 481.10.1 Even and Odd Components of a Signal 491.10.2 Properties of Discrete-Time Even and Odd Signals 491.10.3 Conjugate-Symmetric and Conjugate-Antisymmetric Signals 541.11 Bounded Signal, Absolutely Summable Signal, and Square-summable Signal 561.12 Discrete-Time Systems 561.13 Basic SystemProperties 571.13.1 Linear and Nonlinear Systems 571.13.2 Time-Varying and Time-Invariant Systems (or Shift-Invariant Systems) 631.13.3 Causal Systems 671.13.4 Stable Systems 681.13.5 Systems with andWithoutMemory 701.13.6 Invertibility and Inverse Systems 711.13.7 Passive and Lossless Systems 721.14 Examples 721.15 MATLAB Programs 961.16 Summary 1021.17 Multiple Choice Questions 1031.18 Problems 1051.19 Answers toMultiple Choice Questions 1072. Sampling and Quantization2.1 Introduction 22.2 Sampling 22.3 Sampling Theorem for Low-Pass Signals 32.3.1 Aliasing or SpectrumFolding 62.4 Sampling Techniques 142.5 Impulse Sampling or Ideal Sampling or Instantaneous Sampling 152.6 Natural Sampling or Chopper Sampling 162.7 Flat-Top Sampling 182.7.1 Aperture Effect 212.8 Reconstruction of a signal fromits Samples using Interpolation 222.8.1 Zero-Order-Hold Interpolation 242.8.2 First-Order-Hold Interpolation (or Linear Interpolation) 262.9 Sampling of Sinusoidal Signals 272.10 Sampling Theorem for Band-Pass Signals 322.10.1 Reconstruction of Bandpass Signal 352.11 Quantization 392.11.1 UniformQuantizers 392.11.2 Quantization Error and Quantization Noise 402.11.3 Signal-to-Quantization Noise Ratio (SQNR) 422.11.4 SQNR for Sinusoidal Signals 422.11.5 NonuniformQuantizer (Lloyd-Max Quantizers) 432.12 Sampling of Discrete-Time Signals 462.12.1 Decimation or Down-Sampling 492.12.2 Interpolation or Up-Sampling 512.12.3 Fractional Delays 542.13 Relationship Between DTFT and CTFT 572.14 Examples 592.15 MATLAB Programs 632.16 Summary 672.17 Multiple Choice Questions 692.18 Problems 702.19 Answers to Multiple Choice Questions 713. Convolution and Correlation3.1 Introduction 33.2 The Discrete-Time LTI systems: The Convolution Sum 43.2.1 The Impulse Response (or Unit Sample Response) 43.2.2 The Convolution Sum 43.2.3 GraphicalMethod for the Convolution Sum 83.2.4 Analytical Method (using convolution sumexpression) 123.3 Properties of Convolution Sum 163.3.1 Commutative Property 163.3.2 Associative Property 173.3.3 Distributive Property 183.3.4 Shift Property 193.3.5 Convolution with an Impulse 203.3.6 Width Property 203.3.7 SumProperty 223.4 Convolution of Finite-Length Signals 243.4.1 TabulationMethod 253.4.2 Multiplication Method 273.5 System Response to Periodic Inputs 283.6 Relations between LTI system Properties and the Impulse Response 313.6.1 LTI Systems with and withoutMemory 313.6.2 Causality for LTI Systems 323.6.3 Stability for LTI Systems 333.6.4 Invertibility for LTI Systems 343.6.5 The Unit Step Response of an LTI Systems 353.7 Correlation of Signals 403.7.1 Crosscorrelation Sequence of Discrete-Time Energy Signals 403.7.2 Crosscorrelation Sequence of Power Signals 413.7.3 Autocorrelation Sequence of Discrete-time Signals 423.7.4 Properties of Crosscorrelation and Autocorrelation Sequences 443.8 Examples 463.9 MATLAB Programs 563.10 Summary 633.11 Multiple Choice Questions 643.12 Problems 653.13 Answers toMultiple Choice Questions 674. 4 Discrete-Time Fourier Series4.1 Introduction 44.2 Discrete-Time Fourier Series (DTFS) 54.2.1 Evaluation of DTFS Coefficient 64.2.2 Magnitude and Phase Spectrum of Discrete-Time Periodic Signals (FourierSpectra)4.3 Properties of DTFS 144.3.1 Linearity 154.3.2 Time Shifting 154.3.3 Frequency Shifting 164.3.4 Time Reversal 164.3.5 Time Scaling or Time Expansion 174.3.6 Periodic Convolution 184.3.7 Multiplication 194.3.8 First Difference 204.3.9 Running Sum or Accumulation 204.3.10 Conjugation and Conjugate Symmetry 214.3.11 Parseval's Relation 244.4 Systems with Periodic Inputs4.5 Examples 264.6 MATLAB Programs 374.7 Summary 414.8 Multiple Choice Questions 424.9 Problems 434.10 Answers toMultiple Choice Questions 445. 5 Discrete-Time Fourier Transform5.1 Introduction 55.2 Fourier Transform Representation of Aperiodic Discrete-Time Signals 65.3 Periodicity of the DTFT 95.4 Convergence of DTFT 95.4.1 Gibbs phenomenon 115.5 Properties of Discrete-Time Fourier Transform 245.5.1 Linearity 255.5.2 Time Shifting 255.5.3 Frequency Shifting 275.5.4 Time Reversal 285.5.5 Time Expansion 295.5.6 Differencing in Time Domain 295.5.7 Differentiation in Frequency Domain 305.5.8 Convolution Property 325.5.9 Accumulation Property 345.5.10 Multiplication (orModulation orWindowing) Property 355.5.11 Conjugation and Conjugate Symmetry 365.5.12 Parseval's Relation 415.6 Some Important Results 425.7 Fourier Transformof Periodic Signals 475.8 Signal Transmission Through LTI Systems 505.8.1 Response to Complex Exponentials 515.8.2 Response to Sinusoidal Signals 535.8.3 Response to a Causal Exponential Sequence 555.8.4 Linear and Nonlinear Phase 625.8.5 Phase Delay and Group Delay 635.9 Ideal and Practical Filters 705.9.1 Paley-Wiener Criterion 735.10 Energy Spectral Density (ESD) 785.10.1 Relationship Between Input and Output Energy Spectral Densities of an LTI System 795.10.2 Relation of ESD to Autocorrelation 795.11 Power Spectral Density (PSD) 795.11.1 Relationship Between Input and Output Power Spectral Densities of an LTI System 805.11.2 Relation of PSD to Autocorrelation 815.12 Examples 815.13 MATLAB Programs 985.14 Summary 1065.15 Multiple Choice Questions 1075.16 Problems 1085.17 Answers to Multiple Choice Questions 1106. The z-Transform6.1 Introduction 66.2 Bilateral (Two-sided) z-Transform 76.2.1 Inverse z-Transform 76.3 Relationship Between z-Transform and Discrete-Time Fourier Transform 86.4 z-plane 96.4.1 Poles and Zeros 106.5 Region-of-Convergence for z-Transforms 116.6 Properties of ROC 156.7 Relationship Between Laplace Transform and z-transform (s to z-plane Mapping) 266.8 Relationship Between z-transformand DTFS 296.9 Properties of the z-Transform 296.9.1 Linearity 296.9.2 Time Shifting 316.9.3 Scaling in the z-Domain 326.9.4 Time Reversal 346.9.5 Differentiation in the z-Domain 356.9.6 Time Expansion 406.9.7 Convolution Property 436.9.8 Correlation Property 456.9.9 Accumulation Property 476.9.10 First Difference 496.9.11 Conjugation and Conjugate Symmetry 506.10 z-Transformof Causal Periodic Signals 516.11 Inversion of the z-Transform536.11.1 Contour Integration Method (or ResidueMethod) 536.11.2 Power Series Expansion Method (or Long Division Method) 576.11.3 Partial Fraction ExpansionMethod626.12 Analysis and Characterization of LTI Systems using the z-Transform 716.12.1 The Transfer Function and Difference-Equation System Description 726.12.2 Impulse Response and Step response 726.12.3 Causality 776.12.4 Stability 796.12.5 Stability of a Causal LTI System 806.13 The Unilateral (One-Sided) z-Transform 856.14 Properties of unilateral Z-Transform 896.14.1 Linearity 896.14.2 Scaling in the z-Domain 896.14.3 Differentiation in the z-Domain 906.14.4 Time Expansion 906.14.5 Conjugation Property 906.14.6 Convolution Property 906.14.7 Accumulation Property 916.14.8 Time-Delay (Right-Shift) Property 926.14.9 Time-Advance (Left-Shift) Property 956.14.10 First Difference 976.14.11 Initial-Value Theorem 976.14.12 Final-Value Theorem 996.14.13 Solving Difference Equations using the Unilateral z-Transform 1026.14.14 Zero-Input Response and Zero-State Response 1066.14.15Natural Response and Forced Response 1076.14.16Transient Response and Steady-State Response 1086.15 Block Diagrams Representation 1146.15.1 Cascade Interconnection 1146.15.2 Parallel Interconnection 1156.15.3 Feedback Interconnection 1166.16 Some Application of z-Transformin Signal Processing 1166.16.1 Pole-Zero Description of Discrete-Time Systems 1166.16.2 Frequency Response Estimation 1176.16.3 Frequency Used in Discrete-Time Systems 1176.16.4 Causality and Stability Considerations 1196.16.5 Difference Equations 1196.16.6 Applications in Digital Filter Design 1206.16.7 Realization Structures for Digital Filters 1206.17 Examples 1206.18 MATLAB Programs 1376.19 Summary 1406.20 Multiple Choice Questions 1406.21 Problems 1426.22 Answers toMultiple Choice Questions 1447. Filter Concepts7.1 Introduction 77.2 Frequency Response and Filter Characteristics 87.2.1 Phase Delay and Group delay 97.2.2 Geometric Evaluation of Frequency Response 97.3 Zero-Phase Filter 127.3.1 Zero Locations of Zero-Phase FIR Transfer Functions 137.4 Linear-Phase Filter 147.5 Simple FIR Digital Filters 147.5.1 Lowpass FIR Digital Filter 147.5.2 Highpass FIR Digital Filter 167.5.3 Bandpass FIR Digital Filter 187.5.4 Bandstop (Notch) FIR Digital Filter 207.6 Simple IIR Digital Filters 227.6.1 Lowpass IIR Digital Filter 237.6.2 Highpass IIR Digital Filter 247.6.3 Bandpass IIR Digital Filter 267.6.4 Bandstop IIR Digital Filter 277.7 Allpass Filters 287.7.1 Properties of an allpass filter 307.8 Minimum-Phase, Maximum-Phase and Non-minimum ( or Mixed) Phase Systems 327.8.1 Invertibility and Inverse System 367.8.2 Minimum-phase and Allpass Decomposition 377.9 System Identification and Deconvolution 387.9.1 The Cepstrumand Homomorphic Deconvolution 397.10 Averaging Filters 417.10.1 Zeros of Averaging Filters 427.11 Comb Filters 427.12 Digital Resonators 457.13 Notch Filters 477.14 Digital Sinusoidal Oscillators (Sinusoid Generators) 507.14.1 Digital Sine-Cosine Generators 527.15 Digital Differentiator 547.16 Digital Hilbert Transformer 577.17 Examples 597.18 MATLAB Programs 727.19 Summary 827.20 Multiple Choice Questions 837.21 Problems 857.22 Answers toMultiple Choice Questions 868. Discrete Fourier Transform (DFT)8.1 Introduction 88.2 Frequency Domain Sampling (Sampling of DTFT) 98.3 The Discrete Fourier Transform(DFT) and its Inverse 138.3.1 Derivation of Inverse DFT (IDFT) 168.3.2 Magnitude and Phase of DFT 178.3.3 Zero Padding 248.4 DFT as a Linear Transformation (Matrix Formulation) 288.4.1 Twiddle factor (WN) and its Properties 308.5 Properties of the DFT 338.5.1 Periodicity 348.5.2 Linearity 348.5.3 Circular Time Shifting 358.5.4 Circular Frequency Shifting 408.5.5 Circular Time Reversal (Circular Folding or Circular Flipping) 438.5.6 Conjugation and Conjugate Symmetry (Symmetry Properties) 478.5.7 Duality 518.5.8 Circular Convolution (Multiplication of Two DFTs) 548.5.9 Circular Correlation 628.5.10 Multiplication (orModulation) Property 638.5.11 Parseval's Relation 638.6 Some Important Results 648.7 Linear Convolution Using the DFT (Linear Convolution Using Circular Convolution) 688.7.1 Circular Convolution as Linear Convolution with Aliasing 718.8 Filtering of Long Data Sequences Using DFT (Linear Convolution of a Finite Length Sequence with an Infinite length Sequence) (or Fast Convolution) (or Block Convolution) 728.8.1 Overlap-Save Method 738.8.2 Overlap-AddMethod 758.9 The Discrete Cosine Transform(DCT) 798.9.1 Relationship between the DFT and DCT 818.10 DiscreteWalsh Transform(DWT) 838.10.1 Discrete Hadamard Transform(DHT) 848.11 Relationship of the DFT to Other Transforms 858.11.1 Relationship to Discrete-Time Fourier Series (DTFS) 858.11.2 Relationship to Discrete-Time Fourier Transform(DTFT) 868.11.3 Relationship to z-Transform868.12 SpectrumAnalysis Using DFT 878.12.1 Relationship Between DFT and Continuous-Time Fourier Transform (CTFT) 878.12.2 Relationship Between the Frequency Bin k and its Associated Analog Frequency O or f 888.12.3 Selection of Parameters for Signal Processing with the DFT 908.12.4 High Density Spectrum(Zero-Padding) 918.12.5 Spectral Leakage 928.12.6 Spectral Estimation UsingWindow Functions 938.13 Spectral Analysis of Nonstationary Signals 958.13.1 Short-Time Fourier Transform(STFT) 978.14 Examples 978.15 MATLAB Programs 1098.16 Summary 1198.17 Multiple Choice Questions 1208.18 Problems 1218.19 Answers toMultiple Choice Questions 1229. Fast Fourier Transform (FFT)9.1 Introduction 99.2 Computational Complexity of the Direct Computation of the DFT 99.2.1 Symmetry and Periodicity Properties of the Twiddle Factor (WN) 109.2.2 Radix-2 FFT Algorithms 119.3 Decimation-In-Time (DIT) FFT Algorithm 119.3.1 Computational Advantage of the DIT-FFT 169.3.2 In-Place Computation 179.3.3 Bit-Reversal 179.4 Decimation-In-Frequency (DIF) FFT Algorithm 219.4.1 Computational Cost 269.5 Comparison Between DIT and DIF Algorithms 279.6 Inverse DFT Using FFT Algorithms 349.7 A Linear Filtering Approach to Computation of the DFT 379.7.1 The Goertzel Algorithm 379.7.2 The Chirp-z TransformAlgorithm 439.7.3 Dual-Tome Multi-Frequency (DTMF) Tone Detection Using the Goertzel Algorithm 469.8 Examples 489.9 MATLAB Programs 559.10 Summary 589.11 Multiple Choice Questions 599.12 Problems 609.13 Answers toMultiple Choice Questions 6110. 10 Realization of Digital Filters10.1 Introduction 1010.1.1 FIR Filter or All Zero (AZ) or Moving Average (MA) system: 1110.1.2 IIR Filter or All Pole (AP) or Autoregressive (AR) system 1110.1.3 IIR Filter or Pole-Zero (PZ) or Autoregressive, Moving average (ARMA) system 1210.2 Nonrecursive and Recursive Structures 1310.3 Factors that Influence the Choice of Structure 1310.4 Block Diagram Representation and Signal Flow Graph 1410.4.1 Basic Building Blocks 1410.4.2 Advantages in Representing the Digital Filter in Block Diagram Form 1410.4.3 Canonic and Noncanonic Structures 1510.4.4 Equivalent Structures (Transposed Structure) 1510.5 FIR Filter Structures 1510.5.1 Direct Form (Transversal or Tapped-Delay Line) Structure 1610.5.2 Cascade-Form Structure 1710.5.3 Linear-Phase Structure 1810.5.4 Polyphase Structure 2010.5.5 Conversion of Nonrecursive Structure into Recursive Structure 2410.5.6 Frequency Sampling Structure 2610.6 Basic Structures for IIR Systems 3110.6.1 Direct Form I Structure 3210.6.2 Direct-Form II Structure 3410.6.3 Cascade Form Structure 4010.6.4 Parallel From Structure 4210.6.5 Polyphase Structure 4710.7 Lattice Structures 5110.7.1 Advantages of Lattice Structures 5310.8 Lattice Structures for FIR Systems (All-Zero Systems) 5310.8.1 Conversion of Lattice Coefficients to Direct-Form Filter Coefficients 5710.8.2 Conversion of Direct-Form Filter Coefficients to Lattice Coefficients 5910.9 Lattice Structures for All-Pole (AP) IIR Systems 6510.9.1 Stability of an All-Pole System (Schur-Cohn Stability Test) 6810.10Lattice Structures for Pole-Zero (PZ) IIR Systems (or Lattice-Ladder Structure) 7010.11 Examples 7510.12 MATLAB Programs 8310.13Summary 8610.14 Multiple Choice Questions 8611. Finite Impulse Response (FIR) Digital Filter11.1 Introduction to Digital Filters 1111.1.1 Advantages and Disadvantages of Digital Filters 1111.1.2 Types of Digital Filters: FIR and IIR Filters 1211.1.3 Difference Between FIR and IIR Filters 1311.2 Desirability of Linear-Phase Filters 1411.2.1 Effect of Phase Distortion 1511.2.2 Condition for a Filter to have a Linear-Phase Response 1611.3 Frequency Response of Linear-Phase FIR Filters 2111.3.1 Type 1: Symmetric Impulse Response with Odd Length (M odd) 2411.3.2 Type 2: Symmetric Impulse Response with Even Length (M Even) 2611.3.3 Type 3: Antisymmetric Impulse Response with Odd Length (M Odd) 2811.3.4 Type 4: Antisymmetric Impulse Response with Even Length (M Even) 3111.3.5 Location of Zeros of Linear Phase FIR Transfer Functions 3411.4 Filter Specifications 3811.4.1 Absolute Specifications 3911.4.2 Relative Specifications 4011.4.3 Continuous-time (Analog) Filter Specifications 4211.4.4 Estimation of FIR Filter Order 4311.5 Impulse Responses of Ideal Filters 4511.5.1 Impulse Response of an Ideal Lowpass Filter 4511.5.2 Impulse Response of an Ideal Highpass Filter 4611.5.3 Impulse Response of an Ideal Bandpass Filter 4811.5.4 Impulse Response of an Ideal Bandstop Filter 4811.6 Design Techniques for Linear-Phase FIR Filters 4911.7 Fourier Series Method 5011.7.1 Gibbs Phenomenon 5211.8 Windowing Method 6211.8.1 Rectangular Window 6311.8.2 Triangular (or Bartlett) Window 7611.8.3 Hann (or Hanning) Window 8111.8.4 Hamming Window 8611.8.5 Blackman Window 9711.8.6 Kaiser Window 11811.8.7 Advantages and Disadvantages of the Window Method 12311.9 Half-Band FIR Filters 12411.10 Design of FIR Digital Differentiators 12711.11 Design of FIR Hilbert Transformers 13511.12 Frequency Sampling Method 14211.12.1 Type-I Design 14311.12.2 Type-II Design 15111.12.3 Transition-band Optimization 15511.13 The Optimal Method 15911.13.1 Minimax Criterion 16011.13.2 Alternation Theorem 16611.13.3 Parks-McClellan Algorithm 16811.13.4 Disadvantages of Optimal Method 17211.14 Comparison of Design Methods for Linear-Phase FIR Filters 17211.15 Examples 17211.16 MATLAB Programs 17511.17 Summary 19311.18 Multiple Choice Questions 19511.19 Problems 19711.20Answers to Multiple Choice Questions 19812. Infinite Impulse Response (IIR) Digital Filter12.1 Introduction 1212.2 Design of IIR Filters from Analog Filters 1312.2.1 Filter Design Steps 1312.3 IIR Filter Design by Approximation of Derivatives 1412.3.1 Backward Difference Algorithm 1412.4 Impulse-Invariant Method 1612.4.1 Relationship Between Analog and Digital Filter Poles 1812.4.2 Relationship Between Analog and Digital Frequency 2212.4.3 Advantages and Disadvantages of Impulse-Invariant Method 2212.5 The Matched z-Transformation 3312.6 Step -Invariant Method 3512.7 Bilinear Transformation Method 3712.7.1 Relationship Between Analog and Digital frequency 3912.7.2 Effect of Warping on the Magnitude and Phase Response 4012.7.3 Prewarping 4012.7.4 Advantages and Disadvantages of Bilinear Transformation Method 4112.7.5 Comparison of Impulse-Invariant and Bilinear Transformations 4112.7.6 Relationship Between Impulse-Invariant and Bilinear Transformations 4112.8 IIR Filter Specifications 5012.9 Specifications of the Lowpass Filter 5112.9.1 Properties of Magnitude-squared Response jHa(j-)j2 5112.10Analog Butterworth Filter 5212.10.1 Determination of Filter Parameters (Order N and Cutoff Frequency -c) ofButterworth Filter 6012.10.2 Design Procedure for Lowpass Digital Butterworth Filters 6312.11Analog Chebyshev Filter 7712.11.1Type I Chebyshev Filter 7712.11.2 Determination of Filter Parameters (Order N and Cut-off Frequency -c) of Chebyshev Filter 8112.11.3 Design Procedure for Lowpass Digital Chebyshev Filters 8512.11.4Type II Chebyshev Filter (Inverse Chebyshev Filter) 9212.11.5 Difference Between Butterworth and Chebyshev Filter 9312.12Frequency (or Spectral) Transformation in the Analog Domain 9412.12.1 Lowpass to Lowpass Transformation 9412.12.2 Lowpass to Highpass Transformation 9512.12.3 Lowpass to Bandpass Transformation 9612.12.4 Lowpass to Bandstop Transformation 9712.13Frequency (or Spectral) Transformation in the Digital Domain 10612.13.1 Lowpass to Lowpass Transformation 10712.13.2 Lowpass to Highpass Transformation 10812.13.3 Lowpass to Bandpass Transformation 10812.13.4 Lowpass to Bandstop Transformation 10912.14Applications 11312.14.1 Digital Audio Equalizer 11312.14.2 Generation and Detection of Dual-Tone Multifrequency Tones Using Goertzel Algorithm 11412.14.3 60-Hz Hum Eliminator and Heart Rate Detection Using Electrocardiography (ECG) 11712.14.4 Timing (or Clock) Recovery for Synchronous Digital Communication System12112.15 Examples 12212.16 MATLAB Programs 12612.17Summary 13312.18 Multiple Choice Questions 13412.19 Problems 13612.20Answers to Multiple Choice Questions 13813. Analysis of Finite Word Length Effects13.1 Introduction 1313.2 Representation of Numbers 1413.2.1 Fixed-Point Representation of Numbers 1513.2.2 Binary Floating-Point Representation of Numbers 1813.3 Quantization 2113.3.1 Truncation 2213.3.2 Rounding 2213.4 Quantization of Fixed-Point Numbers 2613.4.1 Effect of Truncation 2613.4.2 Effect of Rounding 2913.5 Quantization of Floating-Point Numbers 3013.5.1 Effect of Truncation 3113.5.2 Effect of Rounding 3313.6 Coefficient Quantization Error 3413.6.1 Coefficient Sensitivity Analysis of a Second-order Direct Form II Structure 3713.6.2 Analysis of Coefficient Quantization Effects in FIR Filters 4313.7 Quantization in Sampling Analog Signals (A/D Conversion Noise Analysis) 4413.7.1 Quantization NoiseModel 4613.7.2 Signal-to-Quantization Noise Ratio 4713.7.3 Effect of Input Scaling on SNR 4813.7.4 Propagation of Input Quantization Noise to Digital Filter Output 4813.8 Product Quantization Error 5713.8.1 Direct Form I Structure 5813.8.2 Direct Form II Structure 6113.8.3 Product Quantization using Double-Length Accumulator 7813.9 Limit Cycles in IIR Digital Filters 8213.9.1 Zero-Input Limit Cycle 8313.9.2 Dead Band 8413.9.3 Overflow Limit Cycle 8813.9.4 Saturation to Avoid Overflow 8913.9.5 Scaling to Prevent Overflow 9013.10Quantization Effects in Floating-Point Realizations of IIR Digital Filters 10113.10.1First Order IIR Digital Filter 10213.11Quantization Effects in Realizations of FIR Digital Filters 10313.11.1 Quantization Effects in Fixed-Point Realizations of FIR Digital Filters 10413.11.2 Quantization Effects in Floating-Point Realizations of FIR Digital Filters 10513.12Quantization Effects in Discrete Fourier Transform (DFT) Computations 10713.12.1 Quantization Effects in Direct Computation of the DFT 10713.12.2 Quantization Effects in Fixed-Point FFT Algorithms 11013.13 Examples 11213.14 MATLAB Programs 11613.15Summary 11713.16 Multiple Choice Questions 11913.17 Problems 12113.18Answers toMultiple Choice Questions 12314. Multirate Digital Signal Processing14.1 Introduction 1414.1.1 Advantages ofMultirate DSP 1414.2 Decimation 1514.2.1 Time-Domain Characterization 1514.2.2 Frequency-Domain Characterization 1614.2.3 Aliasing Effect 1914.2.4 Anti-aliasing Filter Specifications 2014.3 Interpolation 2214.3.1 Time-Domain Characterization 2214.3.2 Frequency-Domain Characterization 2314.3.3 Anti-imaging Filter Specifications 2514.4 Sampling Rate Conversion by a Rational factor LM 2814.5 Identities (Cascaded Equivalences) 3314.5.1 Identities for the Downsampling 3314.5.2 Identities for the Upsampling 3514.5.3 Upsampler and Downsampler Cascade 3714.6 Computational Requirements 4114.6.1 Efficient Direct Form Structure of a Decimator 4214.6.2 Efficient Direct Form Structure of an Interpolator 4314.7 The Polyphase Decomposition 4414.7.1 FIR Filter Structures Based on Polyphase Decomposition 4414.7.2 Decimation with Polyphase Filters 4614.7.3 Interpolation with Polyphase Filters 4914.7.4 Efficient Rational Sampling Rate Converter with Polyphase Filters 5014.7.5 The Polyphase Identity 5314.8 Application ofMultirate DSP: Design of Narrowband Filters 5414.8.1 Interpolated FIR (IFIR) Filters 5514.9 Multistage Implementation of Sampling Rate Conversion 5914.9.1 Multistage Implementation of Decimator 6014.9.2 Multistage Implementation of Interpolator 6714.9.3 Multistage Implementation of Rational Sampling Rate Converter 6714.9.4 The IFIR Approach forMultistage Implementation 6814.10Nyquist Filters (or Lth-Band Filters) 7414.10.1Half-Band Filters 7414.10.2Lth-Band Filters 7614.11Digital Filter Banks 7914.11.1UniformDFT Filter Bank 8014.11.2Polyphase Implementations of UniformDFT Filter Bank 8114.11.3Application of Multirate DSP: Subband Coding of Speech and Audio Signals 8314.12Two-Channel Quadrature-Mirror Filter (QMF) Bank 8514.12.1Analysis of Two-Channel QMF Bank 8614.13Application ofMultirate DSP: Transmultiplexer 9214.14 Examples 9314.15 MATLAB Programs 9614.16Summary 10214.17 Multiple Choice Questions 10214.18 Problems 10414.19Answers toMultiple Choice Questions 10515. Optimum Linear Filters (Wiener Filters)15.1 Introduction 1515.1.1 Mean-Square Error Criterion 1515.2 The FIRWiener Filter 1715.2.1 Filtering 2015.2.2 Linear Prediction 2715.3 Noncausal IIRWiener Filter 3215.3.1 Filtering 3515.4 Innovations Representation 3715.4.1 Spectral Factorization 3815.5 Causal IIRWiener Filter 3915.6 Deconvolution (or Deblurring) 4415.7 Examples 4715.8 MATLAB Programs 4915.9 Summary 5115.10 Multiple Choice Questions 5215.11 Problems 5215.12Answers toMultiple Choice Questions 5316. Power Spectrum Estimation16.1 Introduction 1616.1.1 Parseval's Theorem 1716.1.2 Performance of Estimators 1916.2 Nonparametric (or Classical) Methods 2016.2.1 The Periodogram 2116.2.2 TheModified Periodogram 2416.2.3 Bartlett's Method: Periodogram Averaging 2516.2.4 Welch's Method: AveragingModified Periodograms 2816.2.5 Blackman-Tukey Approach: Periodogram Smoothing 3016.3 Parametric (or Nonclassical) Methods 3416.3.1 Autoregressive SpectrumEstimation 3616.3.2 Computation of Model Parameters Yule-Walker Equations 3716.3.3 Least-squares (LS)Method and Linear Prediction 3916.3.4 Moving Average SpectrumEstimation 4116.3.5 AutoregressiveMoving Average SpectrumEstimation 4216.4 Eigenvalues and Eigenvectors of the Autocorrelation Matrix 4216.4.1 Properties of Eigenvalues and Eigenvectors 4316.5 Eigenanalysis Algorithms for SpectrumEstimation 4716.5.1 HarmonicModel 4716.5.2 Eigen-Decomposition of the Autocorrelation Matrix 4816.5.3 Pisarenko Harmonic Decomposition Method 5916.5.4 MUSIC Algorithm 6216.6 Examples 6416.7 MATLAB Programs 6616.8 Summary 7216.9 Multiple Choice Questions 7316.10 Problems 7416.11Answers toMultiple Choice Questions 7417. Introduction to Digital Signal Processors (DSPs)17.1 Introduction 1717.2 Evolution of Digital Signal Processors 1817.2.1 DSP Algorithms mold DSP Architectures 1817.2.2 FastMultipliers 1817.2.3 Multiple Execution Units 1817.2.4 Efficient memory Accesses 1917.2.5 Data Format 2017.2.6 Zero-Overhead Looping 2017.2.7 Streamlined I/O 2117.2.8 Specialized Instruction Set 2117.3 Digital Signal Processor Architecture 2117.3.1 Von Neumann Architecture 2217.3.2 Harvard Architecture 2317.3.3 Super Harvard Architecture (SHARC) 2417.4 Digital Signal Processor Hardware Units 2417.4.1 Multiplier and Accumulator (MAC) Unit 2417.4.2 Shifters 2417.4.3 Address Generators 2617.5 Fixed-Point and Floating-Point Format 2617.6 Fixed-Point Digital Signal Processor 2717.7 Floating-Point Digital Signal Processor 2717.8 Pipelining 2817.9 Memory Access schemes in DSPs 2917.9.1 Multiple Access Memory 2917.9.2 Multiport memory 2917.10 Very Long InstructionWord (VLIW) Architecture 2917.10.1Advantages 3017.10.2Disadvantages 3117.11AddressingModes 3117.11.1Implied Addressing 3117.11.2Immediate Addressing 3117.11.3Memory-Direct Addressing 3217.11.4Register-Direct Addressing 3217.11.5Register-Indirect Addressing 3217.11.6Bit-Reversed Addressing 3217.11.7Circular Addressing 3217.12The TMS320 Family 3317.12.1 TMS320 C2X Generation 3317.12.2 TMS320 C3X Generation 3417.12.3 TMS320 C4X Generation 3417.12.4 TMS320 C5X Generation 3517.12.5Overview of TMS 320 C6713 DSP 3517.13 Interfacing17.13.1 External Memory Interfacing17.13.2 Serial-port Interfacing17.13.3 Parallel-port Interfacing17.13.4 Host-port Interfacing 1063SummaryMultiple Choice QuestionsQuestions 36Answers to Multiple Choice QuestionsBibliographyIndex