Digital Signal Processing: System Analysis and Design

by Paulo S. R. Diniz , Eduardo A. B. da Silva , Sergio L. Netto

• ISBN13: 9780521781756
• ISBN10: 0521781752
• Format: Hardcover
• Copyright: 2002-05-13
• Publisher: Cambridge University Press

Summary

Digital signal processing lies at the heart of the communications revolution and is an essential element of key technologies such as mobile phones and the Internet. This book covers all the major topics in digital signal processing (DSP) design and analysis, supported by MatLab examples and other modelling techniques. The authors explain clearly and concisely why and how to use digital signal processing systems; how to approximate a desired transfer function characteristic using polynomials and ratio of polynomials; why an appropriate mapping of a transfer function on to a suitable structure is important for practical applications; and how to analyse, represent and explore the trade-off between time and frequency representation of signals. An ideal textbook for students, it will also be a useful reference for engineers working on the development of signal processing systems.

Author Biography

Eduardo A. B. da Silva is an Associate Professor at the undergraduate Department of Electronics and Computer Engineering at the Federal University of Rio de Janeiro (UFRJ) and at the graduate Program of Electrical Engineering at COPPE/UFRJ.

Table of Contents

Preface	xv
Introduction	1	(4)
Discrete-time systems	5	(31)
Introduction	5	(1)
Discrete-time signals	6	(3)
Discrete-time systems	9	(6)
Linearity	9	(1)
Time invariance	10	(1)
Causality	10	(2)
Impulse response and convolution sums	12	(2)
Stability	14	(1)
Difference equations and time-domain response	15	(4)
Sampling of continuous-time signals	19	(10)
Basic principles	20	(1)
Sampling theorem	20	(9)
Discrete-time signals and systems with MATLAB	29	(1)
Summary	30	(1)
Exercises	30	(6)
The z and Fourier transforms	36	(49)
Introduction	36	(1)
Definition of the z transform	37	(6)
Inverse z transform	43	(10)
Computation based on residue theorem	45	(4)
Computation based on partial-fraction expansions	49	(2)
Computation based on polynomial division	51	(1)
Computation based on series expansion	52	(1)
Properties of the z transform	53	(7)
Linearity	53	(1)
Time-reversal	54	(1)
Time-shift theorem	54	(1)
Multiplication by an exponential	55	(1)
Complex differentiation	55	(1)
Complex conjugation	56	(1)
Real and imaginary sequences	56	(1)
Initial value theorem	57	(1)
Convolution theorem	57	(1)
Product of two sequences	58	(1)
Parseval's theorem	59	(1)
Table of basic z transforms	60	(1)
Transfer functions	60	(3)
Stability in the z domain	63	(3)
Frequency response	66	(6)
Fourier transform	72	(3)
Properties of the Fourier transform	75	(4)
Linearity	75	(1)
Time-reversal	75	(1)
Time-shift theorem	76	(1)
Multiplication by an exponential	76	(1)
Complex differentiation	76	(1)
Complex conjugation	76	(1)
Real and imaginary sequences	76	(1)
Symmetric and antisymmetric sequences	77	(1)
Convolution theorem	78	(1)
Product of two sequences	78	(1)
Parseval's theorem	78	(1)
Transfer functions with MATLAB	79	(2)
Summary	81	(1)
Exercises	81	(4)
Discrete transforms	85	(63)
Introduction	85	(1)
Discrete Fourier transform	86	(6)
Properties of the DFT	92	(8)
Linearity	93	(1)
Time-reversal	93	(1)
Time-shift theorem	93	(1)
Circular frequency-shift theorem (modulation theorem)	94	(1)
Circular convolution in time	95	(1)
Correlation	96	(1)
Real and imaginary sequences	97	(1)
Symmetric and antisymmetric sequences	97	(2)
Parseval's theorem	99	(1)
Relationship between the DFT and the z transform	99	(1)
Digital filtering using the DFT	100	(9)
Linear and circular convolutions	100	(5)
Overlap-and-add method	105	(3)
Overlap-and-save method	108	(1)
Fast Fourier transform	109	(21)
Radix-2 algorithm with decimation in time	112	(9)
Decimation in frequency	121	(1)
Radix-4 algorithm	122	(6)
Algorithms for arbitrary values of N	128	(1)
Alternative techniques for determining the DFT	129	(1)
Other discrete transforms	130	(8)
Discrete cosine transform	130	(4)
A family of sine and cosine transforms	134	(1)
Discrete Hartley transform	135	(2)
Hadamard transform	137	(1)
Other important transforms	138	(1)
Signal representations	138	(103)
Discrete transforms with MATLAB	141	(2)
Summary	143	(1)
Exercises	144	(4)
Digital filters	148	(40)
Introduction	148	(1)
Basic structures of nonrecursive digital filters	148	(11)
Direct form	149	(2)
Cascade form	151	(1)
Linear-phase forms	151	(8)
Basic structures of recursive digital filters	159	(6)
Direct forms	159	(3)
Cascade form	162	(1)
Parallel form	163	(2)
Digital network analysis	165	(5)
State-space description	170	(1)
Basic properties of digital networks	171	(9)
Tellegen's theorem	172	(1)
Reciprocity	173	(1)
Interreciprocity	174	(1)
Transposition	175	(1)
Sensitivity	175	(5)
Digital filter forms with MATLAB	180	(4)
Summary	184	(1)
Exercises	184	(4)
FIR filter approximations	188	(66)
Introduction	188	(1)
Ideal characteristics of standard filters	189	(5)
Lowpass, highpass, bandpass, and bandstop filters	189	(1)
Differentiators	190	(2)
Hilbert transformers	192	(2)
Summary	194	(1)
FIR filter approximation by frequency sampling	194	(8)
FIR filter approximation with window functions	202	(17)
Rectangular window	205	(1)
Triangular windows	205	(1)
Hamming and Hanning windows	206	(1)
Blackman window	207	(2)
Kaiser window	209	(7)
Dolph-Chebyshev window	216	(3)
Maximally flat FIR filter approximation	219	(3)
FIR filter approximation by optimization	222	(18)
Weighted-least-squares method	228	(1)
Chebyshev method	229	(6)
WLS-Chebyshev method	235	(5)
FIR filter approximation with MATLAB	240	(6)
Summary	246	(2)
Exercises	248	(6)
IIR filter approximations	254	(56)
Introduction	254	(1)
Analog filter approximations	255	(19)
Analog filter specification	255	(1)
Butterworth approximation	256	(2)
Chebyshev approximation	258	(3)
Elliptic approximation	261	(3)
Frequency transformations	264	(10)
Continuous-time to discrete-time transformations	274	(11)
Impulse-invariance method	274	(4)
Bilinear transformation method	278	(7)
Frequency transformation in the discrete-time domain	285	(3)
Lowpass to lowpass transformation	285	(1)
Lowpass to highpass transformation	286	(1)
Lowpass to bandpass transformation	286	(1)
Lowpass to bandstop transformation	287	(1)
Variable cutoff filter design	288	(1)
Magnitude and phase approximation	288	(10)
Basic principles	289	(4)
Multi-variable function minimization method	293	(3)
Alternative methods	296	(2)
Time-domain approximation	298	(3)
IIR filter approximation with MATLAB	301	(6)
Summary	307	(1)
Exercises	307	(3)
Finite-precision effects	310	(44)
Introduction	310	(1)
Binary number representation	310	(3)
Fixed-point representations	310	(2)
Floating-point representation	312	(1)
Product quantization	313	(6)
Signal scaling	319	(7)
Coefficient quantization	326	(7)
Deterministic sensitivity criterion	326	(4)
Statistical forecast of the wordlength	330	(3)
Limit cycles	333	(18)
Granular limit cycles	334	(1)
Overflow limit cycles	335	(2)
Elimination of zero-input limit cycles	337	(8)
Elimination of constant-input limit cycles	345	(2)
Forced-response stability of digital filters with nonlinearities due to overflow	347	(4)
Summary	351	(1)
Exercises	351	(3)
Multirate systems	354	(21)
Introduction	354	(1)
Basic principles	354	(1)
Decimation	355	(5)
Interpolation	360	(4)
Examples of interpolators	364	(1)
Rational sampling-rate changes	364	(1)
Inverse operations	365	(1)
Decimation and interpolation for efficient filter implementation	365	(6)
Narrowband FIR filters	366	(2)
Wideband FIR filters with narrow transition bands	368	(3)
Multirate systems with MATLAB	371	(2)
Summary	373	(1)
Exercises	374	(1)
Filter banks and wavelets	375	(78)
Introduction	375	(1)
Filter banks	375	(5)
Decimation of a bandpass signal	376	(1)
Inverse decimation of a bandpass signal	377	(1)
Critically decimated M-band filter banks	378	(2)
Perfect reconstruction	380	(10)
Noble identities	380	(1)
Polyphase decompositions	381	(1)
Commutator models	382	(1)
M-band filter banks in terms of polyphase components	383	(2)
Perfect reconstruction M-band filter banks	385	(4)
Transmultiplexers	389	(1)
General 2-band perfect reconstruction filter banks	390	(4)
QMF filter banks	394	(3)
CQF filter banks	397	(2)
Block transforms	399	(2)
Cosine-modulated filter banks	401	(9)
Lapped transforms	410	(17)
Fast algorithms and biorthogonal LOT	420	(2)
Generalized LOT	422	(5)
Wavelet transforms	427	(15)
Hierarchical filter banks	428	(1)
Wavelets	429	(8)
Scaling functions	437	(1)
Relation between x(t) and x(n)	437	(1)
Relation between the wavelets and the filter coefficients	438	(1)
Regularity	439	(2)
Examples	441	(1)
Filter banks and wavelets with MATLAB	442	(7)
Summary	449	(1)
Exercises	450	(3)
Efficient FIR structures	453	(38)
Introduction	453	(1)
Lattice form	453	(4)
Filter banks using the lattice form	455	(2)
Polyphase form	457	(2)
Frequency-domain form	459	(1)
Recursive running sum form	459	(1)
Realizations with reduced number of arithmetic operations	460	(25)
Prefilter approach	460	(4)
Interpolation approach	464	(3)
Frequency response masking approach	467	(12)
Quadrature approach	479	(6)
Efficient FIR structures with MATLAB	485	(2)
Summary	487	(1)
Exercises	488	(3)
Efficient IIR structures	491	(68)
Introduction	491	(1)
IIR parallel and cascade filters	491	(11)
Parallel form	492	(2)
Cascade form	494	(4)
Error spectrum shaping	498	(3)
Closed-form scaling	501	(1)
State-space sections	502	(15)
Optimal state-space sections	503	(5)
State-space sections without limit cycles	508	(9)
Lattice filters	517	(7)
Wave filters	524	(29)
Motivation	526	(2)
Wave elements	528	(16)
Lattice wave digital filters	544	(9)
Efficient IIR structures with MATLAB	553	(1)
Summary	553	(1)
Exercises	554	(5)
Implementation of DSP systems	559	(35)
Introduction	559	(1)
Basic elements	560	(12)
Properties of the two's-complement representation	560	(1)
Serial adder	561	(2)
Serial multiplier	563	(8)
Parallel adder	571	(1)
Parallel multiplier	572	(1)
Distributed arithmetic implementation	572	(8)
Programmable logic devices	580	(1)
ASIC implementation	581	(5)
Digital signal processors	586	(5)
Analog Devices DSPs	588	(1)
Motorola DSPs	588	(1)
Texas Instruments DSPs	589	(2)
Summary	591	(1)
Exercises	592	(2)
References	594	(10)
Index	604