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Digital Signal Processing

Spectral Computation and Filter Design

Chi-Tsong Chen

Publication Date - November 2000

ISBN: 9780195136388

464 pages
7-1/2 x 9-1/4 inches


Designed for a first course in digital signal processing, Digital Signal Processing: Spectral Computation and Filter Design covers two major topics: the computation of frequency contents of signals and the design of digital filters. While it focuses on basic ideas and procedures and covers the standard topics in the field, this unique text distinguishes itself from competing texts by extensively employing the fast Fourier transform (FFT).

Part 1: Spectral Computation deals with continuous-time (CT), discrete-time (DT), and digital signals; CT and DT Fourier series (frequency components); CT and DT Fourier transforms (frequency spectra); and discrete Fourier transform (DFT) and fast Fourier transform (FFT). Part 2: Digital Filter Design discusses linear time-invariant lumped systems; ideal and practical digital filters; design of FIR digital filters; design of IIR filters; and structures of digital filters.

Digital Signal Processing covers numerous topics not found in similar texts. It:
· Establishes a simplified version of the sampling theorem for periodic signals
· Uses FFT to compute frequency spectra of DT and CT signals and inverse FFT to compute DT and CT signals from their frequency spectra
· Employs FFT to compute the inverse z-transform
· Covers steady-state and transient responses of digital filters and gives an estimated time for a transient response to die out
· Gives a mathematical justification for using an antialiasing analog filter in digital signal processing
· Introduces a discrete least-squares method to design FIR filters
· Presents an analog bandstop transformation that yields better results than ones generated by MATLAB®

Digital Signal Processing features careful definitions of all terminology and a wealth of examples and problems. All numerical examples and most end-of-chapter problems are simple enough to be solved analytically by hand; these results can then be compared with the computer-generated solutions. MATLAB® is an integral part of the text.

Table of Contents

    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
    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
    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