Table of Contents 1 Signals and Signal Processing 1 1.1 Characterization and Classification of Signals 1 1.2 Typical Signal Processing Operations 4 1.3 Examples of Typical Signals 13 1.4 Typical Signal Processing Applications 21 1.5 Why Digital Signal Processing? 29 2 Discrete-Time Signals in the Time Domain 33 2.1 Time-Domain Representation 34 2.2 Operations on Sequences 38 2.3 Operations on Finite-Length Sequences 47 2.4 Typical Sequences and Sequence Representation 54 2.5 The Sampling Process 64 2.6 Correlation of Signals 66 2.7 Random Signals 72 2.8 Summary 73 2.9 Problems 73 2.10 MATLAB Exercises 79 3 Discrete-Time Signals in the Frequency Domain 81 3.1 The Continuous-Time Fourier Transform 81 3.2 The Discrete-Time Fourier Transform 86 3.3 Discrete-Time Fourier Transform Theorems 97 3.4 Energy Density Spectrum of a Discrete-Time Sequence 103 3.5 Band-Limited Discrete-Time Signals 104 3.6 DTFT Computation Using MATLAB 105 3.7 The Unwrapped Phase Function 105 3.8 Digital Processing of Continuous-Time Signals 107 3.9 Sampling of Bandpass Signals 121 3.10 Effect of Sample-and-Hold Operation 123 3.11 Summary 124 3.12 Problems 125 3.13 MATLAB Exercises 134 4 Discrete-Time Systems 135 4.1 Discrete-Time System Examples 135 4.2 Classification of Discrete-Time Systems 141 4.3 Impulse and Step Responses 145 4.4 Time-Domain Characterization of LTI Discrete-Time Systems 146 4.5 Simple Interconnection Schemes 153 4.6 Finite-Dimensional LTI Discrete-Time Systems 156 4.7 Classification of LTI Discrete-Time Systems 164 4.8 Frequency-Domain Representations of LTI Discrete-Time Systems 167 4.9 Phase and Group Delays 174 4.10 Summary 178 4.11 Problems 179 4.12 MATLAB Exercises 187 5 Finite-Length Discrete Transforms 188 5.1 Orthogonal Transforms 188 5.2 The Discrete Fourier Transform 190 5.3 Relation Between the DTFT and the DFT and Their Inverses 194 5.4 Circular Convolution 200 5.5 Classifications of Finite-Length Sequences 205 5.6 DFT Symmetry Relations 210 5.7 Discrete Fourier Transform Theorems 213 5.8 Fourier-Domain Filtering 219 5.9 Computation of the DFT of Real Sequences 221 5.10 Linear Convolution Using the DFT 223 5.11 Summary 234 5.12 Problems 234 5.13 MATLAB Exercises 247 6 z-Transform 249 6.1 Definition 249 6.2 Rational z-Transforms 253 6.3 Region of Convergence of a Rational z-Transform 255 6.4 The Inverse z-Transform 261 6.5 z-Transform Theorems 269 6.6 Computation of the Convolution Sum of Finite-Length Sequences 277 6.7 The Transfer Function 280 6.8 Summary 292 6.9 Problems 292 6.10 MATLAB Exercises 304 7 LTI Discrete-Time Systems in the Transform Domain 305 7.1 Transfer Function Classification Based on Magnitude Characteristics 305 7.2 Transfer Function Classification Based on Phase Characteristics 314 7.3 Types of Linear-Phase FIR Transfer Functions 321 7.4 Simple Digital Filters 332 7.5 Inverse Systems 349 7.6 Summary 353 7.7 Problems 354 7.8 MATLAB Exercises 368 8 Digital Filter Structures 371 8.1 Block Diagram Representation 372 8.2 Equivalent Structures 375 8.3 Basic FIR Digital Filter Structures 376 8.4 Basic IIR Digital Filter Structures 381 8.5 Realization of Basic Structures Using MATLAB 387 8.6 Allpass Filters 390 8.7 IIR Tapped Cascaded Lattice Structures 399 8.8 FIR Cascaded Lattice Structures 404 8.9 Summary 409 8.10 Problems 410 8.11 MATLAB Exercises 423 9 IIR Digital Filter Design 425 9.1 Preliminary Considerations 425 9.2 Bilinear TransformationMethod of IIR Filter Design 430 9.3 Design of Lowpass IIR Digital Filters 435 9.4 Design of Highpass, Bandpass, and Bandstop IIR Digital Filters 437 9.5 Spectral Transformations of IIR Filters 441 9.6 IIR Digital Filter Design Using MATLAB 448 9.7 Summary 451 9.8 Problems 451 9.9 MATLAB Exercises 457 10 FIR Digital Filter Design 459 10.1 Preliminary Considerations 459 10.2 FIR Filter Design Based on Windowed Fourier Series 463 10.3 Computer-Aided Design of Equiripple Linear-Phase FIR Filters 478 10.4 Design of Minimum-Phase FIR Filters 487 10.5 FIR Digital Filter Design Using MATLAB 488 10.6 Summary 504 10.7 Problems 505 10.8 MATLAB Exercises 512 11 DSP Algorithm Implementation 516 11.1 Basic Issues 516 11.2 Structure Simulation and Verification Using MATLAB 527 11.3 Computation of the Discrete Fourier Transform 534 11.4 Fast DFT Algorithms Based on Index Mapping 549 11.5 DFT and IDFT Computation Using MATLAB 557 11.6 Sliding Discrete Fourier Transform 559 11.7 DFT Computation over a Narrow Frequency Band 559 11.8 Summary 564 11.9 Problems 564 11.10 MATLAB Exercises 572 A Analog Lowpass Filter Design 575 A.1 Analog Filter Specifications 575 A.2 Butterworth Approximation 577 A.3 Chebyshev Approximation 579 A.4 Elliptic Approximation 582 A.5 Linear-Phase Approximation 583 A.6 Analog Filter Design Using MATLAB 584 A.7 Analog Lowpass Filter Design Examples 587 A.8 A Comparison of the Filter Types 589 A.9 Anti-Aliasing Filter Design 592 A.10 Reconstruction Filter Design 594 B Design of Analog Highpass, Bandpass, and Bandstop Filters 599 B.1 Analog Highpass Filter Design 599 B.2 Analog Bandpass Filter Design 601 B.3 Analog Bandstop Filter Design 604 Bibliography 605