图书简介
Digital Signal Processing is a comprehensive textbook designed for undergraduate and postgraduate students of engineering for a course on digital signal processing. Divided into 17 Chapters, this text covers basic topics to the advanced topics relevant to the UG curricula. Following the book’s step-by-step approach, students can quickly master the fundamental concepts and applications of DSP.
Dedication iii; Features of the Book iv; Preface vi; Brief Content s x; Discrete-Time Signals and Systems; 1.1 Introduction 1; 1.2 Signals, Systems, and Signal Processing 1.2.1 Basic Elements of a Digital Signal Processing Systems 1.2.2 Advantages of Digital Signal Processing (DSP) over Analog Signal Processing (ASP) 1.2.3 DSP Applications 1.3 Classification of Signals 1.3.1 Continuous-Time and Discrete-Time Signals; 1.3.2 Continuous-Valued and Discrete-Valued Signals 1.3.3 Multichannel andMultidimensional Signals; 1.3.4 Deterministic and RandomSignals; 1.4 Discrete-Time Signal or Sequence; 1.4.1 Finite-Length and Infinite-Length Signal 8; 1.4.2 Right-Sided, Causal, Left-Sided, and Anticausal Signals; 1.5 Basic Operations on Discrete-Time Signals; 1.5.1 Signal Addition Operation; 1.5.2 Scalar Addition Operation; 1.5.3 SignalMultiplication Operation; 1.5.4 ScalarMultiplication Operation; 1.6 Transformations of the Independent Variable (Time); 1.6.1 Time-Shifting; 1.6.2 Time-Scaling (Decimation and Interpolation; 1.6.3 Time-Reversal; 1.6.4 Combined Operations; 1.7 Some Basic Discrete-Time Signals; 1.7.1 Unit Step Signal; 1.7.2 Unit Impulse Signal (or Unit Sample Signal); 1.7.3 Unit Ramp Signal 24; 1.7.4 Discrete-Time Real Exponential Signal 25; 1.7.5 Discrete-Time Sinusoidal Signal 26; 1.7.6 Discrete-Time Complex Exponential Signal 27; 1.8 Periodic and Aperiodic Signals 28; 1.8.1 Properties of Periodic Signals 28; 1.8.2 Periodicity of Discrete-Time Sinusoidal Signals 31; 1.9 Energy and Power Signals 41; 1.10 Even and Odd Signals 48; 1.10.1 Even and Odd Components of a Signal 49; 1.10.2 Properties of Discrete-Time Even and Odd Signals 49; 1.10.3 Conjugate-Symmetric and Conjugate-Antisymmetric Signals 54; 1.11 Bounded Signal, Absolutely Summable Signal, and Square-summable Signal 56; 1.12 Discrete-Time Systems 56; 1.13 Basic SystemProperties 57; 1.13.1 Linear and Nonlinear Systems 57; 1.13.2 Time-Varying and Time-Invariant Systems (or Shift-Invariant Systems) 63; 1.13.3 Causal Systems 67; 1.13.4 Stable Systems 68; 1.13.5 Systems with andWithoutMemory 70; 1.13.6 Invertibility and Inverse Systems 71; 1.13.7 Passive and Lossless Systems 72; 1.14 Examples 72; 1.15 MATLAB Programs 96; 1.16 Summary 102; 1.17 Multiple Choice Questions 103; 1.18 Problems 105; 1.19 Answers toMultiple Choice Questions 107; 2 Sampling and Quantization; 2.1 Introduction 2; 2.2 Sampling 2; 2.3 Sampling Theorem for Low-Pass Signals 3; 2.3.1 Aliasing or SpectrumFolding 6; 2.4 Sampling Techniques 14; 2.5 Impulse Sampling or Ideal Sampling or Instantaneous Sampling 15; 2.6 Natural Sampling or Chopper Sampling 16; 2.7 Flat-Top Sampling 18; 2.7.1 Aperture Effect 21; 2.8 Reconstruction of a signal fromits Samples using Interpolation 22; 2.8.1 Zero-Order-Hold Interpolation 24; 2.8.2 First-Order-Hold Interpolation (or Linear Interpolation) 26; 2.9 Sampling of Sinusoidal Signals 27; 2.10 Sampling Theorem for Band-Pass Signals 32; 2.10.1 Reconstruction of Bandpass Signal 35; 2.11 Quantization 39; 2.11.1 UniformQuantizers 39; 2.11.2 Quantization Error and Quantization Noise 40; 2.11.3 Signal-to-Quantization Noise Ratio (SQNR) 42; 2.11.4 SQNR for Sinusoidal Signals 42; 2.11.5 NonuniformQuantizer (Lloyd-Max Quantizers) 43; 2.12 Sampling of Discrete-Time Signals 46; 2.12.1 Decimation or Down-Sampling 49; 2.12.2 Interpolation or Up-Sampling 51; 2.12.3 Fractional Delays 54; 2.13 Relationship Between DTFT and CTFT 57; 2.14 Examples 59; 2.15 MATLAB Programs 63; 2.16 Summary 67; 2.17 Multiple Choice Questions 69; 2.18 Problems 70; 2.19 Answers to Multiple Choice Questions 71; 3 Convolution and Correlation; 3.1 Introduction 3; 3.2 The Discrete-Time LTI systems: The Convolution Sum 4; 3.2.1 The Impulse Response (or Unit Sample Response) 4; 3.2.2 The Convolution Sum 4; 3.2.3 GraphicalMethod for the Convolution Sum 8; 3.2.4 Analytical Method (using convolution sumexpression) 12; 3.3 Properties of Convolution Sum 16; 3.3.1 Commutative Property 16; 3.3.2 Associative Property 17; 3.3.3 Distributive Property 18; 3.3.4 Shift Property 19; 3.3.5 Convolution with an Impulse 20; 3.3.6 Width Property 20; 3.3.7 SumProperty 22; 3.4 Convolution of Finite-Length Signals 24; 3.4.1 TabulationMethod 25; 3.4.2 Multiplication Method 27; 3.5 System Response to Periodic Inputs 28; 3.6 Relations between LTI system Properties and the Impulse Response 31; 3.6.1 LTI Systems with and withoutMemory 31; 3.6.2 Causality for LTI Systems 32; 3.6.3 Stability for LTI Systems 33; 3.6.4 Invertibility for LTI Systems 34; 3.6.5 The Unit Step Response of an LTI Systems 35; 3.7 Correlation of Signals 40; 3.7.1 Crosscorrelation Sequence of Discrete-Time Energy Signals 40; 3.7.2 Crosscorrelation Sequence of Power Signals 41; 3.7.3 Autocorrelation Sequence of Discrete-time Signals 42; 3.7.4 Properties of Crosscorrelation and Autocorrelation Sequences 44; 3.8 Examples 46; 3.9 MATLAB Programs 56; 3.10 Summary 63; 3.11 Multiple Choice Questions 64; 3.12 Problems 65; 3.13 Answers toMultiple Choice Questions 67; 4 Discrete-Time Fourier Series; 4.1 Introduction 4; 4.2 Discrete-Time Fourier Series (DTFS) 5; 4.2.1 Evaluation of DTFS Coefficient 6; 4.2.2 Magnitude and Phase Spectrum of Discrete-Time Periodic Signals (Fourier; Spectra); 4.3 Properties of DTFS 14; 4.3.1 Linearity 15; 4.3.2 Time Shifting 15; 4.3.3 Frequency Shifting 16; 4.3.4 Time Reversal 16; 4.3.5 Time Scaling or Time Expansion 17; 4.3.6 Periodic Convolution 18; 4.3.7 Multiplication 19; 4.3.8 First Difference 20; 4.3.9 Running Sum or Accumulation 20; 4.3.10 Conjugation and Conjugate Symmetry 21; 4.3.11 Parsevalas Relation 24; 4.4 Systems with Periodic Inputs; 4.5 Examples 26; 4.6 MATLAB Programs 37; 4.7 Summary 41; 4.8 Multiple Choice Questions 42; 4.9 Problems 43; 4.10 Answers toMultiple Choice Questions 44; 5 Discrete-Time Fourier Transform; 5.1 Introduction 5; 5.2 Fourier Transform Representation of Aperiodic Discrete-Time Signals 6; 5.3 Periodicity of the DTFT 9; 5.4 Convergence of DTFT 9; 5.4.1 Gibbs phenomenon 11; 5.5 Properties of Discrete-Time Fourier Transform 24; 5.5.1 Linearity 25; 5.5.2 Time Shifting 25; 5.5.3 Frequency Shifting 27; 5.5.4 Time Reversal 28; 5.5.5 Time Expansion 29; 5.5.6 Differencing in Time Domain 29; 5.5.7 Differentiation in Frequency Domain 30; 5.5.8 Convolution Property 32; 5.5.9 Accumulation Property 34; 5.5.10 Multiplication (orModulation orWindowing) Property 35; 5.5.11 Conjugation and Conjugate Symmetry 36; 5.5.12 Parsevalas Relation 41; 5.6 Some Important Results 42; 5.7 Fourier Transformof Periodic Signals 47; 5.8 Signal Transmission Through LTI Systems 50; 5.8.1 Response to Complex Exponentials 51; 5.8.2 Response to Sinusoidal Signals 53; 5.8.3 Response to a Causal Exponential Sequence 55; 5.8.4 Linear and Nonlinear Phase 62; 5.8.5 Phase Delay and Group Delay 63; 5.9 Ideal and Practical Filters 70; 5.9.1 Paley-Wiener Criterion 73; 5.10 Energy Spectral Density (ESD) 78; 5.10.1 Relationship Between Input and Output Energy Spectral Densities of an; LTI System 79; 5.10.2 Relation of ESD to Autocorrelation 79; 5.11 Power Spectral Density (PSD) 79; 5.11.1 Relationship Between Input and Output Power Spectral Densities of an; LTI System 80; 5.11.2 Relation of PSD to Autocorrelation 81; 5.12 Examples 81; 5.13 MATLAB Programs 98; 5.14 Summary 106; 5.15 Multiple Choice Questions 107; 5.16 Problems 108; 5.17 Answers to Multiple Choice Questions 110; 6 The z-Transform; 6.1 Introduction 6; 6.2 Bilateral (Two-sided) z-Transform 7; 6.2.1 Inverse z-Transform 7; 6.3 Relationship Between z-Transform and Discrete-Time Fourier Transform 8; 6.4 z-plane 9; 6.4.1 Poles and Zeros 10; 6.5 Region-of-Convergence for z-Transforms 11; 6.6 Properties of ROC 15; 6.7 Relationship Between Laplace Transform and z-transform (s to z-plane Mapping) 26; 6.8 Relationship Between z-transformand DTFS 29; 6.9 Properties of the z-Transform 29; 6.9.1 Linearity 29; 6.9.2 Time Shifting 31; 6.9.3 Scaling in the z-Domain 32; 6.9.4 Time Reversal 34; 6.9.5 Differentiation in the z-Domain 35; 6.9.6 Time Expansion 40; 6.9.7 Convolution Property 43; 6.9.8 Correlation Property 45; 6.9.9 Accumulation Property 47; 6.9.10 First Difference 49; 6.9.11 Conjugation and Conjugate Symmetry 50; 6.10 z-Transformof Causal Periodic Signals 51; 6.11 Inversion of the z-Transform53; 6.11.1 Contour Integration Method (or ResidueMethod) 53; 6.11.2 Power Series Expansion Method (or Long Division Method) 57; 6.11.3 Partial Fraction ExpansionMethod62; 6.12 Analysis and Characterization of LTI Systems using the z-Transform 71; 6.12.1 The Transfer Function and Difference-Equation System Description 72; 6.12.2 Impulse Response and Step response 72; 6.12.3 Causality 77; 6.12.4 Stability 79; 6.12.5 Stability of a Causal LTI System 80; 6.13 The Unilateral (One-Sided) z-Transform 85; 6.14 Properties of unilateral Z-Transform 89; 6.14.1 Linearity 89; 6.14.2 Scaling in the z-Domain 89; 6.14.3 Differentiation in the z-Domain 90; 6.14.4 Time Expansion 90; 6.14.5 Conjugation Property 90; 6.14.6 Convolution Property 90; 6.14.7 Accumulation Property 91; 6.14.8 Time-Delay (Right-Shift) Property 92; 6.14.9 Time-Advance (Left-Shift) Property 95; 6.14.10 First Difference 97; 6.14.11 Initial-Value Theorem 97; 6.14.12 Final-Value Theorem 99; 6.14.13 Solving Difference Equations using the Unilateral z-Transform 102; 6.14.14 Zero-Input Response and Zero-State Response 106; 6.14.15Natural Response and Forced Response 107; 6.14.16Transient Response and Steady-State Response 108; 6.15 Block Diagrams Representation 114; 6.15.1 Cascade Interconnection 114; 6.15.2 Parallel Interconnection 115; 6.15.3 Feedback Interconnection 116; 6.16 Some Application of z-Transformin Signal Processing 116; 6.16.1 Pole-Zero Description of Discrete-Time Systems 116; 6.16.2 Frequency Response Estimation 117; 6.16.3 Frequency Used in Discrete-Time Systems 117; 6.16.4 Causality and Stability Considerations 119; 6.16.5 Difference Equations 119; 6.16.6 Applications in Digital Filter Design 120; 6.16.7 Realization Structures for Digital Filters 120; 6.17 Examples 120; 6.18 MATLAB Programs 137; 6.19 Summary 140; 6.20 Multiple Choice Questions 140; 6.21 Problems 142; 6.22 Answers toMultiple Choice Questions 144; 7 Filter Concepts; 7.1 Introduction 7; 7.2 Frequency Response and Filter Characteristics 8; 7.2.1 Phase Delay and Group delay 9; 7.2.2 Geometric Evaluation of Frequency Response 9; 7.3 Zero-Phase Filter 12; 7.3.1 Zero Locations of Zero-Phase FIR Transfer Functions 13; 7.4 Linear-Phase Filter 14; 7.5 Simple FIR Digital Filters 14; 7.5.1 Lowpass FIR Digital Filter 14; 7.5.2 Highpass FIR Digital Filter 16; 7.5.3 Bandpass FIR Digital Filter 18; 7.5.4 Bandstop (Notch) FIR Digital Filter 20; 7.6 Simple IIR Digital Filters 22; 7.6.1 Lowpass IIR Digital Filter 23; 7.6.2 Highpass IIR Digital Filter 24; 7.6.3 Bandpass IIR Digital Filter 26; 7.6.4 Bandstop IIR Digital Filter 27; 7.7 Allpass Filters 28; 7.7.1 Properties of an allpass filter 30; 7.8 Minimum-Phase, Maximum-Phase and Non-minimum ( or Mixed) Phase Systems 32; 7.8.1 Invertibility and Inverse System 36; 7.8.2 Minimum-phase and Allpass Decomposition 37; 7.9 System Identification and Deconvolution 38; 7.9.1 The Cepstrumand Homomorphic Deconvolution 39; 7.10 Averaging Filters 41; 7.10.1 Zeros of Averaging Filters 42; 7.11 Comb Filters 42; 7.12 Digital Resonators 45; 7.13 Notch Filters 47; 7.14 Digital Sinusoidal Oscillators (Sinusoid Generators) 50; 7.14.1 Digital Sine-Cosine Generators 52; 7.15 Digital Differentiator 54; 7.16 Digital Hilbert Transformer 57; 7.17 Examples 59; 7.18 MATLAB Programs 72; 7.19 Summary 82; 7.20 Multiple Choice Questions 83; 7.21 Problems 85; 7.22 Answers toMultiple Choice Questions 86; 8 Discrete Fourier Transform (DFT); 8.1 Introduction 8; 8.2 Frequency Domain Sampling (Sampling of DTFT) 9; 8.3 The Discrete Fourier Transform(DFT) and its Inverse 13; 8.3.1 Derivation of Inverse DFT (IDFT) 16; 8.3.2 Magnitude and Phase of DFT 17; 8.3.3 Zero Padding 24; 8.4 DFT as a Linear Transformation (Matrix Formulation) 28; 8.4.1 Twiddle factor (WN) and its Properties 30; 8.5 Properties of the DFT 33; 8.5.1 Periodicity 34; 8.5.2 Linearity 34; 8.5.3 Circular Time Shifting 35; 8.5.4 Circular Frequency Shifting 40; 8.5.5 Circular Time Reversal (Circular Folding or Circular Flipping) 43; 8.5.6 Conjugation and Conjugate Symmetry (Symmetry Properties) 47; 8.5.7 Duality 51; 8.5.8 Circular Convolution (Multiplication of Two DFTs) 54; 8.5.9 Circular Correlation 62; 8.5.10 Multiplication (orModulation) Property 63; 8.5.11 Parsevalas Relation 63; 8.6 Some Important Results 64; 8.7 Linear Convolution Using the DFT (Linear Convolution Using Circular Convolution) 68; 8.7.1 Circular Convolution as Linear Convolution with Aliasing 71; 8.8 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) 72; 8.8.1 Overlap-Save Method 73; 8.8.2 Overlap-AddMethod 75; 8.9 The Discrete Cosine Transform(DCT) 79; 8.9.1 Relationship between the DFT and DCT 81; 8.10 DiscreteWalsh Transform(DWT) 83; 8.10.1 Discrete Hadamard Transform(DHT) 84; 8.11 Relationship of the DFT to Other Transforms 85; 8.11.1 Relationship to Discrete-Time Fourier Series (DTFS) 85; 8.11.2 Relationship to Discrete-Time Fourier Transform(DTFT) 86; 8.11.3 Relationship to z-Transform86; 8.12 SpectrumAnalysis Using DFT 87; 8.12.1 Relationship Between DFT and Continuous-Time Fourier Transform (CTFT) 87; 8.12.2 Relationship Between the Frequency Bin k and its Associated Analog Frequency O or f 88; 8.12.3 Selection of Parameters for Signal Processing with the DFT 90; 8.12.4 High Density Spectrum(Zero-Padding) 91; 8.12.5 Spectral Leakage 92; 8.12.6 Spectral Estimation UsingWindow Functions 93; 8.13 Spectral Analysis of Nonstationary Signals 95; 8.13.1 Short-Time Fourier Transform(STFT) 97; 8.14 Examples 97; 8.15 MATLAB Programs 109; 8.16 Summary 119; 8.17 Multiple Choice Questions 120; 8.18 Problems 121; 8.19 Answers toMultiple Choice Questions 122; 9 Fast Fourier Transform (FFT); 9.1 Introduction 9; 9.2 Computational Complexity of the Direct Computation of the DFT 9; 9.2.1 Symmetry and Periodicity Properties of the Twiddle Factor (WN) 10; 9.2.2 Radix-2 FFT Algorithms 11; 9.3 Decimation-In-Time (DIT) FFT Algorithm 11; 9.3.1 Computational Advantage of the DIT-FFT 16; 9.3.2 In-Place Computation 17; 9.3.3 Bit-Reversal 17; 9.4 Decimation-In-Frequency (DIF) FFT Algorithm 21; 9.4.1 Computational Cost 26; 9.5 Comparison Between DIT and DIF Algorithms 27; 9.6 Inverse DFT Using FFT Algorithms 34; 9.7 A Linear Filtering Approach to Computation of the DFT 37; 9.7.1 The Goertzel Algorithm 37; 9.7.2 The Chirp-z TransformAlgorithm 43; 9.7.3 Dual-Tome Multi-Frequency (DTMF) Tone Detection Using the Goertzel Algorithm 46; 9.8 Examples 48; 9.9 MATLAB Programs 55; 9.10 Summary 58; 9.11 Multiple Choice Questions 59; 9.12 Problems 60; 9.13 Answers toMultiple Choice Questions 61; 10 Realization of Digital Filters; 10.1 Introduction 10; 10.1.1 FIR Filter or All Zero (AZ) or Moving Average (MA) system: 11; 10.1.2 IIR Filter or All Pole (AP) or Autoregressive (AR) system 11; 10.1.3 IIR Filter or Pole-Zero (PZ) or Autoregressive, Moving average (ARMA) system 12; 10.2 Nonrecursive and Recursive Structures 13; 10.3 Factors that Influence the Choice of Structure 13; 10.4 Block Diagram Representation and Signal Flow Graph 14; 10.4.1 Basic Building Blocks 14; 10.4.2 Advantages in Representing the Digital Filter in Block Diagram Form 14; 10.4.3 Canonic and Noncanonic Structures 15; 10.4.4 Equivalent Structures (Transposed Structure) 15; 10.5 FIR Filter Structures 15; 10.5.1 Direct Form (Transversal or Tapped-Delay Line) Structure 16; 10.5.2 Cascade-Form Structure 17; 10.5.3 Linear-Phase Structure 18; 10.5.4 Polyphase Structure 20; 10.5.5 Conversion of Nonrecursive Structure into Recursive Structure 24; 10.5.6 Frequency Sampling Structure 26; 10.6 Basic Structures for IIR Systems 31; 10.6.1 Direct Form I Structure 32; 10.6.2 Direct-Form II Structure 34; 10.6.3 Cascade Form Structure 40; 10.6.4 Parallel From Structure 42; 10.6.5 Polyphase Structure 47; 10.7 Lattice Structures 51; 10.7.1 Advantages of Lattice Structures 53; 10.8 Lattice Structures for FIR Systems (All-Zero Systems) 53; 10.8.1 Conversion of Lattice Coefficients to Direct-Form Filter Coefficients 57; 10.8.2 Conversion of Direct-Form Filter Coefficients to Lattice Coefficients 59; 10.9 Lattice Structures for All-Pole (AP) IIR Systems 65; 10.9.1 Stability of an All-Pole System (Schur-Cohn Stability Test) 68; 10.10Lattice Structures for Pole-Zero (PZ) IIR Systems (or Lattice-Ladder Structure) 70; 10.11 Examples 75; 10.12 MATLAB Programs 83; 10.13Summary 86; 10.14 Multiple Choice Questions 86; 11 Finite Impulse Response (FIR) Digital Filter; 11.1 Introduction to Digital Filters 11; 11.1.1 Advantages and Disadvantages of Digital Filters 11; 11.1.2 Types of Digital Filters: FIR and IIR Filters 12; 11.1.3 Difference Between FIR and IIR Filters 13; 11.2 Desirability of Linear-Phase Filters 14; 11.2.1 Effect of Phase Distortion 15; 11.2.2 Condition for a Filter to have a Linear-Phase Response 16; 11.3 Frequency Response of Linear-Phase FIR Filters 21; 11.3.1 Type 1: Symmetric Impulse Response with Odd Length (M odd) 24; 11.3.2 Type 2: Symmetric Impulse Response with Even Length (M Even) 26; 11.3.3 Type 3: Antisymmetric Impulse Response with Odd Length (M Odd) 28; 11.3.4 Type 4: Antisymmetric Impulse Response with Even Length (M Even) 31; 11.3.5 Location of Zeros of Linear Phase FIR Transfer Functions 34; 11.4 Filter Specifications 38; 11.4.1 Absolute Specifications 39; 11.4.2 Relative Specifications 40; 11.4.3 Continuous-time (Analog) Filter Specifications 42; 11.4.4 Estimation of FIR Filter Order 43; 11.5 Impulse Responses of Ideal Filters 45; 11.5.1 Impulse Response of an Ideal Lowpass Filter 45; 11.5.2 Impulse Response of an Ideal Highpass Filter 46; 11.5.3 Impulse Response of an Ideal Bandpass Filter 48; 11.5.4 Impulse Response of an Ideal Bandstop Filter 48; 11.6 Design Techniques for Linear-Phase FIR Filters 49; 11.7 Fourier Series Method 50; 11.7.1 Gibbs Phenomenon 52; 11.8 Windowing Method 62; 11.8.1 Rectangular Window 63; 11.8.2 Triangular (or Bartlett) Window 76; 11.8.3 Hann (or Hanning) Window 81; 11.8.4 Hamming Window 86; 11.8.5 Blackman Window 97; 11.8.6 Kaiser Window 118; 11.8.7 Advantages and Disadvantages of the Window Method 123; 11.9 Half-Band FIR Filters 124; 11.10 Design of FIR Digital Differentiators 127; 11.11 Design of FIR Hilbert Transformers 135; 11.12 Frequency Sampling Method 142; 11.12.1 Type-I Design 143; 11.12.2 Type-II Design 151; 11.12.3 Transition-band Optimization 155; 11.13 The Optimal Method 159; 11.13.1 Minimax Criterion 160; 11.13.2 Alternation Theorem 166; 11.13.3 Parks-McClellan Algorithm 168; 11.13.4 Disadvantages of Optimal Method 172; 11.14 Comparison of Design Methods for Linear-Phase FIR Filters 172; 11.15 Examples 172; 11.16 MATLAB Programs 175; 11.17 Summary 193; 11.18 Multiple Choice Questions 195; 11.19 Problems 197; 11.20Answers to Multiple Choice Questions 198; 12 Infinite Impulse Response (IIR) Digital Filter; 12.1 Introduction 12; 12.2 Design of IIR Filters from Analog Filters 13; 12.2.1 Filter Design Steps 13; 12.3 IIR Filter Design by Approximation of Derivatives 14; 12.3.1 Backward Difference Algorithm 14; 12.4 Impulse-Invariant Method 16; 12.4.1 Relationship Between Analog and Digital Filter Poles 18; 12.4.2 Relationship Between Analog and Digital Frequency 22; 12.4.3 Advantages and Disadvantages of Impulse-Invariant Method 22; 12.5 The Matched z-Transformation 33; 12.6 Step -Invariant Method 35; 12.7 Bilinear Transformation Method 37; 12.7.1 Relationship Between Analog and Digital frequency 39;
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