Preface
1. Introduction
1.1. Continuous-Time (CT), Discrete-Time (DT), and Digital Signals
1.2. Representation of Digital Signals
1.3. A/D and D/A Conversions
1.4. Comparison of Digital and Analog Techniques
1.5. Applications of Digital Signal Processing
1.6. Scope of the Book
PART 1: SPECTRAL COMPUTATION
2. CT and DT Fourier Series--Frequency components
2.1. Introduction
2.2. Frequency and Frequency Range of Sinusoidal Sequences
2.3. Frequencies of CT Sinusoids and Their Sampled Sequences
2.4. Continuous-Time Fourier Series (CTFS)
2.5. Discrete-Time Fourier Series (DTFS)
2.6. FFT Computation of DTFS Coefficients
2.7. FFT Computation of CTFS Coefficients
2.8. Average Power and Its Computation
2.9. Concluding Remarks
3. CT and DT Fourier Transforms--Frequency Spectra
3.1. Introduction
3.2. CT Fourier Transform (CTFT)
3.3. Properties of Frequency Spectra
3.4. Distribution of Energy in Frequencies
3.5. Effects of Truncation
3.6. DT Fourier Transform (DTFT)
3.7. Effects of Truncation
3.8. Nyquist Sampling Theorem
3.9. Time-limited Bandlimited Theorem
4. DFT and FFT--Spectral Computation
4.1. Introduction
4.2. Discrete Fourier Transform (DFT)
4.3. Properties of DFT
4.4. Fast Fourier Transform (FFT)
4.5. Spectral Computation of Finite Sequences
4.6. Spectral Computation of CT Signals
4.7. Computing DT Signals from Spectra
4.8. Computing Energy Using FFT
4.9. Concluding Remarks
PART 2: FILTER DESIGN
5. Linear Time-Invariant Lumped Systems
5.1. Introduction
5.2. Linearity and Time Invariance
5.3. LTIL Systems--Difference Equations
5.4. z-Transform
5.5. Transfer Functions
5.6. Stability
5.7. Frequency Response
5.8. Continuous-Time LTIL Systems
5.9. CT Transfer Function, Stability, and Frequency Response
5.10. Concluding Remarks
6. Ideal and Some Practical Digital Filters
6.1. Introduction
6.2. Ideal Digital Filters
6.3. Realizability
6.4. First-Order Digital Filters
6.5. Reciprocal Roots and All-Pass Filters
6.6. Miscellaneous Topics
6.7. Analog Ideal Low-Pass Filters
7. Design of FIR Filters
7.1. Introduction
7.2. Classification of Linear-Phase FIR Filters
7.3. Least-Square Optimal Filters--Direct Truncation
7.4. Window Method
7.5. Desired Filters with Specified Transition Bands
7.6. Discrete Least-Squares Optimal FIR Filters
7.7. Minimax Optimal FIR Filters
7.8. Design of Digital Differentiators
7.9. Hilbert Transformers
7.10. A Design Example
8. Design of IIR Filter Design
8.1. Introduction
8.2. Difficulties in Direct IIR Filter Design
8.3. Design of Analog Prototype Filters
8.4. Analog Frequency Transformations
8.5. Impulse Invariance Method
8.6. Bilinear Transformation
8.7. Analog-Prototype-to-Digital Transformations
8.8. Comparisons with FIR Filters
9. Structures of Digital Filters
9.1. Introduction
9.2. Direct Form of FIR Filters
9.3. DFT of Periodic Convolutions
9.4. Direct and Canonical Forms of IIR Filters
9.5. Effects of Filter Coefficient Quantizations
9.6. Cascade and Parallel Implementations
Appendix: The Impulse
References
Index