Digital signal processing:system analysis and design

《数字信号处理：系统分析与设计(英文版·第2版)》

preface

introduction

1 discrete-time signals and systems

1.1 introduction

1.2 discrete-time signals

1.3 discrete-time systems

1.3.1 linearity

1.3.2 time invariance

1.3.3 causality

1.3.4 impulse response and convolution sums

1.3.5stability

1.4 difference equations and time-domain response

1.4.1 recursive x nonrecursive systems

1.5 solving difference equations

1.5.1 computing impulse responses

1.6 sampling of continuous-time signals

1.6.1 basic principles

1.6.2 sampling theorem

1.7 random signals

.1.7.1 random variable

1.7.2 random processes

1.7.3 filtering a random signal

1.8 do-it-yourselfi discrete-time signals and systems

1.9 discrete-time signals and systems with matlab

1.10summary

1.11exercises

2 the z and fourier transforms

2.1 introduction

2.2 definition of the z transform

2.3 inverse z transform

2.3.1 computation based on residue theorem

2.3.2 computation based on partial-fraction expansions

2.3.4 computation based on series expansion

2.4 properties of the z transform

2.4.1 linearity

2.4.2 time reversal

2.4.3 time-shift theorem

2.4.4 multiplication by an exponential

2.4.5 complex differentiation

2.4.6 complex conjugation

2.4.7 real and imaginary sequences

2.4.8 initial-value theorem

2.4.9 convolution theorem

2.4.10product of two sequences

2.4.11parseval's theorem

2.4.12table of basic z transforms

2.5 transfer functions

2.6 stability in the z domain

2.7 frequency response

2.8 fourier transform

2.9 properties of the fourier transform

2.9.1 linearity

2.9.2 time reversal

2.9.3 time-shift theorem

2.9.4 multiplication by a complex exponential (frequency shift,modulation)

2.9.5 complex differentiation

2.9.6 complex conjugation

2.9.7 real and imaginary sequences

2.9.8 symmetric and antisymmetric sequences

2.9.9 convolution theorem

2.9.10product of two sequences

2.9.11parseval's theorem

2.10fourier transform for periodic sequences

2.11random signals in the transform domain

2.11.1power spectral density

2.11.2whitenoise

2.12do-it-yourself: the z and fourier transforms

2.13the z and fourier transforms with matlab

2.14summary

2.15exercises

3discrete transforms

3.1 introduction

3.2 discrete fourier transform

3.3 properties of the dft

3.3.1 linearity

3.3.2 time reversal

3.3.3 time-shift theorem

3.3.4 circular frequency-shift theorem (modulation theorem)

3.3.5 circular convolution in time

3.3.6 correlation

3.3.7 complex conjugation

3.3.8 real and imaginary sequences

3.3.9 symmetric and antisymmetric sequences

3.3.10parseval's theorem

3.3.11relationship between the dft and the z transform

3.4 digital filtering using the dft

3.4.1 linear and circular convolutions

3.4.2 overlap-and-add method

3.4.3 overlap-and-save method

3.5 fast fourier transform

3.5.1 radix-2 algorithm with decimation in time

3.5.2 decimation in frequency

3.5.3 radix-4 algorithm

3.5.4 algorithms for arbitrary values of n

3.5.5 alternative techniques for determining the dft

3.6 other discrete transforms

3.6.1 discrete transforms and parseval's theorem

3.6.2 discrete transforms and orthogonality

3.6.3 discrete cosine transform

3.6.4 a family of sine and cosine transforms

3.6.5 discrete hartley transform

3.6.6 hadamard transform

3.6.7 other important transforms

3.7 signal representations

3.7.1 laplace transform

3.7.2 the z transform

3.7.3 fourier transform (continuous time)

3.7.4 fourier transform (discrete time)

3.7.5 fourier series

3.7.6 discrete fourier transform

3.8 do-it-yourself: discrete transforms

3.9 discrete transforms with matlab

3.10summary

3.11exercises

4digital filters

4.1 introduction

4.2 basic structures of nonrecursive digital filters

4.2.1 direct form

4.2.2 cascade form

4.2.3 linear-phase forms

4.3 basic structures of recursive digital filters

4.3.1 direct forms

4.3.2 cascade form

4.3.3 parallel form

4.4 digital network analysis

4.5 state-space description

4.6 basic properties of digital networks

4.6.1 tcllegen's theorem

4.6.2 reciprocity

4.6.3 interreciprocity

4.6.4 transposition

4.6.5 sensitivity

4.7 useful building blocks

4.7.1 second-order building blocks

4.7.2 digital oscillators

4.7.3 comb filter

4.8 do-it-yourself: digital filters

4.9 digital filter forms with matlab

4.10summary

4.11exercises

5fir filter approximations

5. l introduction

5.2 ideal characteristics of standard filters

5.2.1 lowpass, highpass, bandpass, and bandstop filters

5.2.2 differentiators

5.2.3 hilbert transformers

5.2.4 summary

5.3 fir filter approximation by frequency sampling

5.4 fir filter approximation with window functions

5.4.1 rectangular window

5.4.2 triangular windows

5.4.3 hamming and hann windows

5.4.4 blackman window

5.4.5 kaiser window

5.4.6 dolph-chebyshev window

5.5 maximally flat fir filter approximation

5.6 fir filter approximation by optimization

5.6.1 weighted least-squares method

5.6.2 chebyshev method

5.6.3 wls-chebyshev method

5.7 do-it-yourselfi fir filter approximations

5.8 fir filter approximation with matlab

5.9 summary

5.10exercises

6iir filter approximations

6.1 introduction

6.2 analog filter approximations

6.2.1 analog filter specification

6.2.2 butterworth approximation

6.2.3 chebyshev approximation

6.2.4 elliptic approximation

6.2.5 frequency transformations

6.3 continuous-time to discrete-time transformations

6.3.1 impulse-invariance method

6.3.2 bilinear transformation method

6.4 frequency transformation in the discrete-time domain

6.4.1 lowpass-to-lowpass transformation

6.4.2 lowpass-to-highpass transformation

6.4.3 lowpass-to-bandpass transformation

6.4.4 lowpass-to-bandstop transformation

6.4.5 variable-cutoff filter design

6.5 magnitude and phase approximation

6.5.1 basic principles

6.5.2 multivariable function minimization method

6.5.3 alternative methods

6.6 time-domain approximation

6.6.1 approximate approach

6.7 do-it-yourself: iir filter approximations

6.8 iir filter approximation with matlab

6.9 summary

6.10exercises

7 spectral estimation

7.1 introduction

7.2 estimation theory

7.3 nonparametric spectral estimation

7.3.1 periodogram

7.3.2 periodogram variations

7.3.3 minimum-variance spectral estimator

7.4 modeling theory

7.4.1 rational transfer-function models

7.4.2 yule-walker equations

7.5 parametric spectral estimation

7.5.1 linear prediction

7.5.2 covariance method

7.5.3 autocorrelation method

7.5.4 levinson-durbin algorithm

7.5.5 burg's method

7.5.6 relationship of the levinson-durbin algorithm toa lattice structure

7.6 wiener filter

7.7 other methods for spectral estimation

7.8 do-it-yourself: spectral estimation

7.9 spectral estimation with matlab

7.t0summary

7.11exercises

8 multirate systems

8.1 introduction

8.2 basic principles

8.3 decimation

8.4 interpolation

8.4.1 examples of interpolators

8.5 rational sampling-rate changes

8.6 inverse operations

8.7 noble identities

8.8 polyphase decompositions

8.9 commutator models

8.10decimation and interpolation for efficient filter implementation

8.10.1narrowband fir filters

8.10.2wideband fir filters with narrow transition bands

8.11overlapped block filtering

8.11.1nonoverlapped case

8.11.2overlapped input and output

8.11.3fast convolution structure i

8.11.4fast convolution structure ii

8.12random signals in multirate systems

8.12.1interpolated random signals

8.12.2decimated random signals

8.13do-it-yourselfi multirate systems

8.14multirate systems with matlab

8.15summary

8.16exercises

9 filter banks

9.1 introduction

9.2 filter banks

9.2.1 decimation of a bandpass signal

9.2.2 inverse decimation of a bandpass signal

9.2.3 critically decimated m-band filter banks

9.3 perfect reconstruction

9.3.1 m-band filter banks in terms of polyphase components

9.3.2 perfect reconstruction m-band filter banks

9.4 analysis of m-band filter banks

9.4.1 modulation matrix representation

9.4.2 time-domain analysis

9.4.3 orthogonality and biorthogonality in filter banks

9.4.4 transmultiplexers

9.5 general two-band perfect reconstruction filter banks

9.6 qmf filter banks

9.7 cqf filter banks

9.8 block transforms

9.9 cosine-modulated filter banks

9.9.1 the optimization problem in the design of cosine-modulated filter banks

9.10lapped transforms

9.10.1fast algorithms and biorthogonal lot

9.10.2generalized lot

9.11do-it-yourself: filter banks

9.12filter banks with matlab

9.13summary

9.14exercises

10 wavelet transforms

10.1introduction

10.2wavelet transforms

10.2.1hierarchical filter banks

10.2.2wavelets

10.2.3scaling functions

10.3relation between x(t) and x(n)

10.4wavelet transforms and time-frequency analysis

10.4.1the short-time fourier transform

10.4.2the continuous-time wavelet transform

10.4.3sampling the continuous-time wavelet transform: the discrete wavelet transform

10.5multiresolution representation

10.5.1biorthogonal multiresolution representation

10.6wavelet transforms and filter banks

10.6.1relations between the filter coefficients

10.7regularity

10.7.1additional constraints imposed on the filter banksdue to the regularity condition

10.7.2a practical estimate of regularity

10.7.3number ofvanishing moments

10.8examples of wavelets

10.9wavelet transforms of images

10.10 wavelet transforms of finite-length signals

10.10.1 periodic signal extension

10.10.2 symmetric signal extensions

10.11 do-it-yourself: wavelet transforms

10.12 wavelets with matlab

10.13 summary

10.14 exercises

11 finite-precision digital signal processing

11.1introduction

11.2binary number representation

11.2.1fixed-point representations

11.2.2signed power-of-two representation

11.2.3floating-point representation

11.3basic elements

11.3.1properties of the two's-complement representation

11.3.2serial adder

11.3.3serial multiplier

11.3.4parallel adder

11.3.5parallel multiplier

11.4distributed arithmetic implementation

11.5product quantization

11.6signal scaling

11.7coefficient quantization

11.7.1deterministic sensitivity criterion

11.7.2statistical forecast of the wordlength

11.8limit cycles

11.8.1granular limit cycles

11.8.2overflow limit cycles

11.8.3elimination of zero-input limit cycles

11.8.4elimination of constant-input limit cycles

11.8.5forced-response stability of digital filters with nonlinearities due to overflow

11.9do-it-yourself: finite-precision digital signal processing

11.10 finite-precision digital signal processing with matlab

11.11 summary

11.12 exercises

12 efficient fir structures

12.1introduction

12.2lattice form

12.2.1filter banks using the lattice form

12.3polyphase form

12.4frequency-domain form

12.5recursive running sum form

12.6modified-sinc filter

12.7realizations with reduced number of arithmetic operations

12.7.1prefilter approach

12.7.2interpolation approach

12.7.3frequency-response masking approach

12.7.4quadrature approach

12.8do-it-yourself: efficient fir structures

12.9efficient fir structures with matlab

12.10 summary

12.11 exercises

13 efficient iir structures

13.1introduction

13.2iir parallel and cascade filters

13.2.1parallel form

13.2.2cascade form

13.2.3error spectrum shaping

13.2.4closed-form scaling

13.3state-space sections

13.3.1optimal state-space sections

13.3.2state-space sections without limit cycles

13.4lattice filters

13.5doubly complementary filters

13.5.1qmf filter bank implementation

13.6wave filters

13.6.1motivation

13.6.2wave elements

13.6.3lattice wave digital filters

13.7do-it-yourself: efficient iir structures

13.8efficient iir structures with matlab

13.9summary

13.10 exercises

references

index