Digital Signal Processing Spectral Computation and Filter Design

by Chen, Chi-Tsong

• ISBN13: 9780195136388
• ISBN10: 0195136381
• Format: Hardcover
• Copyright: 2000-11-30
• Publisher: Oxford University Press

Summary

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 thestandard 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 FilterDesign 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: DT Establishes a simplified version of the sampling theorem for periodic signals DT Uses FFT to compute frequency spectra of DT and CT signals and inverse FFT to compute DT and CT signals from their frequency spectra DT Employs FFT to compute the inverse z-transform DT Covers steady-state and transient responses of digital filters and gives an estimated time for a transient response to die out DT Gives a mathematical justification for using an antialiasing analog filter in digital signal processing DT Introduces a discrete least-squares method to design FIR filters DT Presents an analog bandstop transformation that yields better results than ones generated by MATLABRG 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.MATLABRG is an integral part of the text.

Table of Contents

Preface	xiii
Introduction	1	(20)
Continuous-Time (CT), Discrete-Time (DT), and Digital Signals	1	(3)
Plotting of DT Signals	3	(1)
Representation of Digital Signals	4	(2)
A/D and D/A Conversions	6	(5)
Comparison of Digital and Analog Techniques	11	(1)
Applications of Digital Signal Processing	12	(2)
Scope of the Book	14	(7)
Spectral Computation	15	(3)
Digital Filter Design	18	(3)
PART 1 Spectral Computation
CT and DT Fourier Series--Frequency Components	21	(61)
Introduction	21	(1)
Frequency of CT Sinusoids	22	(1)
Frequency and Frequency Range of Sinusoidal Sequences	22	(6)
Frequencies of CT Sinusoids and Their Sampled Sequences	28	(6)
Applications	30	(1)
Recovering a Sinusoid from Its Sampled Sequence	31	(3)
Continuous-Time Fourier Series (CTFS)	34	(11)
Distribution of Average Power in Frequencies	42	(1)
Are Phases Important?	43	(2)
Discrete-Time Fourier Series (DTFS)	45	(9)
Range of Frequency Index m	51	(1)
Time Shifting	52	(2)
FFT Computation of DTFS Coefficients	54	(5)
Rearranging the Output of the FFT	55	(4)
FFT Computation of CTFS Coefficients	59	(16)
Frequency Aliasing due to Time Sampling	66	(3)
Selecting N to Have Negligible Frequency Aliasing	69	(6)
Average Power and Its Computation	75	(3)
Concluding Remarks	78	(4)
Problems	78	(4)
CT and DT Fourier Transforms--Frequency Spectra	82	(50)
Introduction	82	(1)
CT Fourier Transform (CTFT)	82	(10)
Frequency Spectrum of CT Periodic Signals	89	(3)
Properties of Frequency Spectra	92	(7)
Boundedness and Continuity	92	(1)
Even and Odd	93	(3)
Time Shifting	96	(1)
Frequency Shifting	96	(1)
Time Compression and Expansion	97	(2)
Distribution of Energy in Frequencies	99	(2)
Effects of Truncation	101	(5)
Gibbs Phenomenon	103	(3)
DT Fourier Transform (DTFT)	106	(8)
Frequency Spectrum of DT Periodic Signals	113	(1)
Effects of Truncation	114	(3)
Nyquist Sampling Theorem	117	(9)
Frequency Aliasing due to Time Sampling	122	(4)
Time-limited Bandlimited Theorem	126	(6)
Practical Reconstruction of x(t) from x(nT)	127	(1)
Problems	128	(4)
DFT and FFT--Spectral Computation	132	(59)
Introduction	132	(1)
Discrete Fourier Transform (DFT)	132	(12)
Relationship between DFT and DTFS	140	(1)
Inverse DFT and Inverse DTFT--Time Aliasing due to Frequency Sampling	141	(3)
Properties of DFT	144	(2)
Even and Odd	144	(1)
Periodic Shifting	145	(1)
Fast Fourier Transform (FFT)	146	(9)
Other FFT and DSP Processors	150	(2)
Real Sequences	152	(3)
Spectral Computation of Finite Sequences	155	(8)
Padding with Zeros	156	(3)
Spectral Computation of Infinite Sequences	159	(4)
Spectral Computation of CT Signals	163	(11)
Spectral Computation of CT Periodic Signals	171	(3)
Computing DT Signals from Spectra	174	(8)
Computing CT Signals from Spectra	179	(3)
Computing Energy Using FFT	182	(2)
Concluding Remarks	184	(7)
Problems	186	(5)
PART 2 Digital Filter Design
Linear Time-Invariant Lumped Systems	191	(61)
Introduction	191	(1)
Linearity and Time Invariance	192	(6)
LTI Systems--Convolutions	193	(5)
LTIL Systems--Difference Equations	198	(6)
Recursive and Nonrecursive Difference Equations	202	(1)
Sampling Period and Real-Time Processing	203	(1)
z-Transform	204	(11)
Inverse z-Transform	210	(3)
FFT Computation of the Inverse z-Transform	213	(2)
Transfer Functions	215	(10)
Poles and Zeros	218	(4)
Transfer Functions of FIR and IIR Filters	222	(1)
DT Fourier Transform and z-Transform	223	(2)
Stability	225	(3)
The Jury Test	226	(2)
Frequency Response	228	(11)
Infinite Time	234	(1)
Frequency Response and Frequency Spectrum	235	(2)
Alternative Derivation of Frequency Responses	237	(2)
Continuous-Time LTIL Systems	239	(3)
Laplace Transform and z-Transform	241	(1)
CT Transfer Function, Stability, and Frequency Response	242	(5)
Measuring CT Frequency Responses	245	(2)
Concluding Remarks	247	(5)
Problems	248	(4)
Ideal and Some Practical Digital Filters	252	(42)
Introduction	252	(1)
Ideal Digital Filters	252	(1)
Realizability	253	(8)
Filter Specifications	257	(2)
Digital Processing of Analog Signals	259	(2)
First-Order Digital Filters	261	(14)
Second-Order Digital Filters	270	(5)
Reciprocal Roots and All-Pass Filters	275	(5)
Miscellaneous Topics	280	(6)
Comb Filters	280	(1)
Sinusoid Generators	281	(3)
Goertzel Algorithm	284	(2)
Analog Ideal Low-Pass Filters	286	(8)
Why Antialiasing Filters?	289	(3)
Problems	292	(2)
Design of FIR Filters	294	(61)
Introduction	294	(1)
Classification of Linear-Phase FIR Filters	295	(7)
Least-Squares Optimal Filters-Direct Truncation	302	(3)
Window Method	305	(5)
Desired Filters with Specified Transition Bands	310	(6)
Design by Frequency Sampling	313	(3)
Discrete Least-Squares Optimal FIR Filters	316	(11)
Integral Least-Squares Optimal FIR Filters	324	(3)
Minimax Optimal FIR Filters	327	(5)
Design of Digital Differentiators	332	(8)
Hilbert Transformers	340	(9)
From FIR Low-Pass Filters to Hilbert Transformers	346	(3)
A Design Example	349	(6)
Problems	352	(3)
Design of IIR Filters	355	(43)
Introduction	355	(1)
Difficulties in Direct IIR Filter Design	356	(2)
Design of Analog Prototype Filters	358	(6)
Analog Frequency Transformations	364	(10)
Impulse Invariance Method	374	(12)
Digital Frequency Transformations	379	(7)
Bilinear Transformation	386	(4)
Analog-Prototype-to-Digital Transformations	390	(4)
Comparisons with FIR Filters	394	(4)
Problems	395	(3)
Structures of Digital Filters	398	(33)
Introduction	398	(1)
Direct Form of FIR Filters	399	(4)
Cascade Form	400	(3)
DFT of Periodic Convolutions	403	(6)
FFT Computation of FIR Filters	404	(4)
Convolution of Finite and Infinite Sequences	408	(1)
Direct and Canonical Forms of IIR Filters	409	(7)
Implementation Using State-Space Equations	414	(2)
Effects of Filter Coefficient Quantizations	416	(3)
Dead Band and Limit Cycle	417	(2)
Cascade and Parallel Implementations	419	(12)
Implementation of Second-Order Sections	424	(3)
Problems	427	(4)
Appendix: The Impulse	431	(4)
References	435	(2)
Index	437