| Preface |  | xi |  | 
| Introduction |  | 1 | (5) | 
| 
|  | Discrete-Time Signals and Systems |  |  | 6 | (39) | 
|  |  | 6 | (2) | 
| 
|  | Discrete-Time Signals-Sequences |  |  | 8 | (3) | 
| 
|  | Linear Shift-Invariant Systems |  |  | 11 | (2) | 
|  |  | 13 | (3) | 
| 
|  | Linear Constant-Coefficient Difference Equations |  |  | 16 | (2) | 
| 
|  | Frequency-Domain Representation of Discrete-Time Systems and Signals |  |  | 18 | (6) | 
| 
|  | Some Symmetry Properties of the Fourier Transform |  |  | 24 | (2) | 
| 
|  | Sampling of Continuous-Time Signals |  |  | 26 | (4) | 
| 
|  | Two-Dimensional Sequences and Systems |  |  | 30 | (15) | 
|  |  | 34 | (1) | 
|  |  | 35 | (10) | 
|  |  | 45 | (42) | 
|  |  | 45 | (1) | 
|  |  | 45 | (7) | 
|  |  | 52 | (6) | 
| 
|  | z-Transform Theorems and Properties |  |  | 58 | (9) | 
|  |  | 67 | (6) | 
| 
|  | Two-Dimensional Z-Transform |  |  | 73 | (14) | 
|  |  | 77 | (1) | 
|  |  | 78 | (9) | 
| 
|  | The Discrete Fourier Transform |  |  | 87 | (49) | 
|  |  | 87 | (1) | 
| 
|  | Representation of Periodic Sequences-The Discrete Fourier Series |  |  | 88 | (3) | 
| 
|  | Properties of the Discrete Fourier Series |  |  | 91 | (4) | 
| 
|  | Summary of Properties of the DFS Representation of Periodic Sequences |  |  | 95 | (1) | 
|  |  | 96 | (3) | 
| 
|  | Fourier Representation of Finite-Duration Sequences--The Discrete Fourier Transform |  |  | 99 | (2) | 
| 
|  | Properties of the Discrete Fourier Transform |  |  | 101 | (9) | 
| 
|  | Summary of Properties of the Discrete Fourier Transform |  |  | 110 | (1) | 
| 
|  | Linear Convolution Using the Discrete Fourier Transform |  |  | 110 | (5) | 
| 
|  | Two-Dimensional Discrete Fourier Transform |  |  | 115 | (21) | 
|  |  | 121 | (1) | 
|  |  | 121 | (15) | 
| 
|  | Flow Graph and Matrix Representation of Digital Filters |  |  | 136 | (59) | 
|  |  | 136 | (1) | 
| 
|  | Signal Flow Graph Representation of Digital Networks |  |  | 137 | (6) | 
| 
|  | Matrix Representation of Digital Networks |  |  | 143 | (5) | 
| 
|  | Basic Network Structures for IIR Systems |  |  | 148 | (5) | 
|  |  | 153 | (2) | 
| 
|  | Basic Network Structures for FIR Systems |  |  | 155 | (10) | 
| 
|  | Parameter Quantization Effects |  |  | 165 | (8) | 
| 
|  | Tellegen's Theorem for Digital Filters and Its Applications |  |  | 173 | (22) | 
|  |  | 181 | (1) | 
|  |  | 182 | (13) | 
| 
|  | Digital Filter Design Techniques |  |  | 195 | (89) | 
|  |  | 195 | (2) | 
| 
|  | Design of IIR Digital Filters from Analog Filters |  |  | 197 | (14) | 
| 
|  | Design Examples: Analog-Digital Transformation |  |  | 211 | (19) | 
| 
|  | Computer-Aided Design of IIR Digital Filters |  |  | 230 | (7) | 
| 
|  | Properties of FIR Digital Filters |  |  | 237 | (2) | 
| 
|  | Design of FIR Filters Using Windows |  |  | 239 | (11) | 
| 
|  | Computer-Aided Design of FIR Filters |  |  | 250 | (18) | 
| 
|  | A Comparison of IIR and FIR Digital Filters |  |  | 268 | (16) | 
|  |  | 269 | (2) | 
|  |  | 271 | (13) | 
| 
|  | Computation of the Discrete Fourier Transform |  |  | 284 | (53) | 
|  |  | 284 | (3) | 
|  |  | 287 | (4) | 
| 
|  | Decimation-in-Time FFT Algorithms |  |  | 291 | (11) | 
| 
|  | Decimation-in-Frequency FFT Algorithms |  |  | 302 | (5) | 
| 
|  | FFT Algorithms for N a Composite Number |  |  | 307 | (8) | 
| 
|  | General Computational Considerations in FFT Algorithms |  |  | 315 | (6) | 
| 
|  | Chirp Z-Transform Algorithm |  |  | 321 | (16) | 
|  |  | 326 | (2) | 
|  |  | 328 | (9) | 
| 
|  | Discrete Hilbert Transforms |  |  | 337 | (39) | 
|  |  | 337 | (2) | 
| 
|  | Real- and Imaginary-part Sufficiency for Causal Sequences |  |  | 339 | (6) | 
|  |  | 345 | (8) | 
| 
|  | Hilbert Transform Relations for the DFT |  |  | 353 | (5) | 
| 
|  | Hilbert Transform Relations for Complex Sequences |  |  | 358 | (18) | 
|  |  | 365 | (2) | 
|  |  | 367 | (9) | 
|  |  | 376 | (28) | 
|  |  | 376 | (1) | 
| 
|  | A Discrte-Time Random Process |  |  | 377 | (5) | 
|  |  | 382 | (6) | 
| 
|  | Spectrum Representations of Infinite-Energy Signals |  |  | 388 | (3) | 
| 
|  | Response of Linear Systems to Random Signals |  |  | 391 | (13) | 
|  |  | 395 | (1) | 
|  |  | 395 | (9) | 
| 
|  | Effects of Finite Register Length in Digital Signal Processing |  |  | 404 | (76) | 
|  |  | 404 | (2) | 
| 
|  | Effect on Number Representation on Quantization |  |  | 406 | (7) | 
| 
|  | Quantization in Sampling Analog Signals |  |  | 413 | (5) | 
| 
|  | Finite-Register-Length Effects in Realizations of IIR Digital Filters |  |  | 418 | (20) | 
| 
|  | Finite-Register-Length Effects in Realizations of FIR Digital Filters |  |  | 438 | (6) | 
| 
|  | Effects of Finite Register Length in Discrete Fourier Transform Computations |  |  | 444 | (36) | 
|  |  | 462 | (2) | 
|  |  | 464 | (16) | 
| 
|  | Homomorphic Signal Processing |  |  | 480 | (52) | 
|  |  | 480 | (1) | 
| 
|  | Generalized Superposition |  |  | 481 | (3) | 
| 
|  | Multiplicative Homomorphic System |  |  | 484 | (3) | 
| 
|  | Homomorphic Image Processing |  |  | 487 | (3) | 
| 
|  | Homomorphic Systems for Convolution |  |  | 490 | (10) | 
| 
|  | Properties of the Complex Cepstrum |  |  | 500 | (7) | 
| 
|  | Computational Realizations of the Characteristic Syste D |  |  | 507 | (4) | 
| 
|  | Applications of Homomorphic Deconvolution |  |  | 511 | (21) | 
|  |  | 527 | (2) | 
|  |  | 529 | (3) | 
| 
|  | Power Spectrum Estimation |  |  | 532 | (45) | 
|  |  | 532 | (1) | 
| 
|  | Basic Principles of Estimation Theory |  |  | 533 | (6) | 
| 
|  | Estimates of the Autocovariance |  |  | 539 | (2) | 
| 
|  | The Periodogram as an Estimate of the Power Spectrum |  |  | 541 | (7) | 
| 
|  | Smoothed Spectrum Estimators |  |  | 548 | (6) | 
| 
|  | Estimates of the Cross Covariance and Cross Spectrum |  |  | 554 | (1) | 
| 
|  | Application of the FFT in Spectrum Estimation |  |  | 555 | (7) | 
| 
|  | Example of Spectrum Estimation |  |  | 562 | (15) | 
|  |  | 571 | (1) | 
|  |  | 571 | (6) | 
| Index |  | 577 |  |