Digital Signal Processing: Principles and Applications

Cover
Half-title
Reviews
Title page
Copyright information
Dedication
Contents
Preface
	Noteworthy features of the book
		Accessible, comprehensive text
		Good balance of theory and application
		Multi-level integration of Matlab®
		Examples and illustrations
	Detailed description of the book's chapters
1 Discrete-time signals and systems
	Introduction
	1.1 Two signal processing paradigms
	1.2 Advantages of digital signal processing
	1.3 Applications of DSP
	1.4 Signals
		1.4.1 Signal classification
		1.4.2 Discrete-time signals
			Table
			Plot
			Sequences generated by functions
			Features of sequences
			Sequence representation in Matlab
	1.5 Basic operations on signals
		1.5.1 Shift
		1.5.2 Flip
		1.5.3 Flip and shift
		1.5.4 Time decimation
		1.5.5 Time expansion
		1.5.6 Operation on multiple sequences
	1.6 Basic sequences
		1.6.1 Impulse
			Use of discrete-time impulses in the synthesis and analysis of signals
		1.6.2 Unit step
			Relation between the step and the impulse
			Use of the step as a switch
		1.6.3 Pulse
		1.6.4 Power-law sequences
		1.6.5 Sinusoidal sequences
			Discrete-time frequency is different from continuous-time frequency
			Not all discrete-time sinusoidal sequences are periodic
			Not all discrete-time frequencies are unique
		1.6.6 Complex exponential sequences
		1.6.7 Sequence classification
			Energy and power signals
			Real and imaginary sequences
			Even and odd sequences
	1.7 Systems
		1.7.1 Discrete-time scalar multiplier
		1.7.2 Offset
		1.7.3 Squarer
		1.7.4 Shift
		1.7.5 Moving-window average
		1.7.6 Summer
		1.7.7 Switch
		1.7.8 Linear constant-coefficient difference equation (LCCDE)
	1.8 Linearity
		1.8.1 The additivity property
		1.8.2 The scaling property
		1.8.3 Discrete-time scalar multiplier
		1.8.4 Offset
		1.8.5 Squarer
		1.8.6 Shift
		1.8.7 Moving-window average
			Scaling property
		1.8.8 Summer
		1.8.9 Switch
		1.8.10 Linear constant-coefficient difference equation
		1.8.11 The ''zero-in, zero-out'' property of linear systems
	1.9 Time invariance
		1.9.1 Discrete-time scalar multiplier
		1.9.2 Offset
		1.9.3 Squarer
		1.9.4 Shift
		1.9.5 Moving-window average
		1.9.6 Summer
		1.9.7 Switch
		1.9.8 Linear constant-coefficient difference equation (LCCDE)
	1.10 Causality
		1.10.1 Discrete-time scalar multiplier
		1.10.2 Offset
		1.10.3 Squarer
		1.10.4 Shift
		1.10.5 Moving-window average
		1.10.6 Summer
		1.10.7 Switch
		1.10.8 Linear constant-coefficient difference equation (LCCDE)
	1.11 Stability
		1.11.1 Discrete-time scalar multiplier
		1.11.2 Offset
		1.11.3 Squarer
		1.11.4 Shift
		1.11.5 Moving-window average
		1.11.6 Summer
		1.11.7 Switch
		1.11.8 Linear constant-coefficient difference equation (LCCDE)
	Summary
	Problems
		Problem 1-1
		Problem 1-2
		Problem 1-3
		Problem 1-4
		Problem 1-5
		Problem 1-6
		Problem 1-7
		Problem 1-8
		Problem 1-9
		Problem 1-10
		Problem 1-11
		Problem 1-12
		Problem 1-13
		Problem 1-14
		Problem 1-15
		Problem 1-16
		Problem 1-17
		Problem 1-18
		Problem 1-19
		Problem 1-20
		Problem 1-21
		Problem 1-22
		Problem 1-23
		Problem 1-24
		Problem 1-25
		Problem 1-26
		Problem 1-27
		Problem 1-28
		Problem 1-29
		Problem 1-30
		Problem 1-31
		Problem 1-32
		Problem 1-33
		Problem 1-34
		Problem 1-35
2 Impulse response
	Introduction
	2.1 FIR and IIR systems
		2.1.1 Finite impulse response (FIR) systems
		2.1.2 Infinite impulse response (IIR) systems
		2.1.3 Response of a system to a flipped and shifted impulse
			Response of a system to a shifted impulse
			Response to a scaled impulse
			Impulse response of a linear time-invariant system
	2.2 Convolution
		2.2.1 Direct-summation method
		2.2.2 Flip-and-shift method
		2.2.3 Convolution examples
			Step response
			Response to a pulse
	2.3 Properties of convolution
		2.3.1 The commutative property
		2.3.2 The associative property
		2.3.3 The distributive property
	2.4 Stability and causality
		2.4.1 Stability
			Stability of FIR systems
			Stability of IIR systems
		2.4.2 Causality
	2.5 Convolution reinterpreted
		2.5.1 Convolution as polynomial multiplication
		2.5.2 Convolution using Matlab
		2.5.3 Convolution as matrix multiplication
	2.6 Deconvolution
		Deconvolution as polynomial division
		Deconvolution using Matlab
		Deconvolution via matrix inversion
	2.7 Convolution of long sequences
		2.7.1 Overlap-add method
		2.7.2 Overlap-save method
	2.8 Implementation issues
	Summary
	Problems
		Problem 2-1
		Problem 2-2
		Problem 2-3
		Problem 2-4
		Problem 2-5
		Problem 2-6
		Problem 2-7
		Problem 2-8
		Problem 2-9
		Problem 2-10
		Problem 2-11
		Problem 2-12
		Problem 2-13
		Problem 2-14
		Problem 2-15
		Problem 2-16
		Problem 2-17
		Problem 2-18
		Problem 2-19
		Problem 2-20
		Problem 2-21
		Problem 2-22
		Problem 2-23
		Problem 2-24
		Problem 2-25
		Problem 2-26
		Problem 2-27
		Problem 2-28
		Problem 2-29
		Problem 2-30
		Problem 2-31
		Problem 2-32
		Problem 2-33
		Problem 2-34
		Problem 2-35
		Problem 2-36
3 Discrete-time Fourier transform
	Introduction
	3.1 Complex exponentials and sinusoids
		3.1.1 Response of LTI systems to complex exponentials
			Complex exponentials and the system function
		3.1.2 Response of linear time-invariant systems to sinusoids
	3.2 Discrete-time Fourier transform (DTFT)
		3.2.1 Orthogonality of complex exponential sequences
		3.2.2 Definition and derivation
		3.2.3 Notation of the DTFT
		3.2.4 Existence of the DTFT
		3.2.5 The system function (again)
		3.2.6 Periodicity of the DTFT
		3.2.7 DTFT of finite-length sequences
		3.2.8 DTFT of infinite-length sequences
	3.3 Magnitude and phase description of the DTFT
		3.3.1 Magnitude and phase of the DTFT of an impulse
		3.3.2 Essential phase discontinuities
	3.4 Important sequences and their transforms
	3.5 Symmetry properties of the DTFT
		3.5.1 Time reversal
		3.5.2 Conjugate symmetry and antisymmetry
			Real sequences
			Imaginary sequences
		3.5.3 Even and odd symmetry
			Even sequences
			Odd sequences
		3.5.4 Consequences of symmetry
			Real-and-even sequences
			Real-and-odd sequences
			Imaginary sequences
		3.5.5 Complex sequences
		3.5.6 Symmetry summary
	3.6 Response of a system to sinusoidal input
	3.7 Linear-phase systems
		3.7.1 Causal symmetric sequences
		3.7.2 Causal antisymmetric sequences
		3.7.3 Time delay and group delay
			Time delay
			Group delay
	3.8 The inverse discrete-time Fourier transform
		Finite-length sequences
		Infinite-length sequences
	3.9 Using Matlab to compute and plot the DTFT
	3.10 DTFT properties
		3.10.1 Linearity
		3.10.2 Delay (shifting) property
		3.10.3 Complex modulation (frequency shift) property
			Modulation by (-1)n
		3.10.4 Convolution
		3.10.5 Using the convolution property of the DTFT to do filtering
			Method #1: direct time-domain convolution
			Method #2: convolution by multiplication of transforms
		3.10.6 Deconvolution and system identification using the convolution property
			Deconvolution
			System identification
		3.10.7 Convolution properties
		3.10.8 Understanding filtering in the frequency domain
		3.10.9 Multiplication (windowing) property
		3.10.10 Time- and band-limited systems
			A time-limited system cannot be band-limited
			A band-limited system cannot be time-limited
		3.10.11 Spectral and temporal ambiguity
		3.10.12 Time-reversal property
		3.10.13 Differentiation property
		3.10.14 Parseval's theorem
		3.10.15 DC- and π-value properties
		3.10.16 Using the DTFT to solve linear constant-coefficient difference equations
		3.10.17 summary of DTFT properties
	3.11 The relation between the DTFT and the Fourier series
	Summary
	Problems
		Problem 3-1
		Problem 3-2
		Problem 3-3
		Problem 3-4
		Problem 3-5
		Problem 3-6
		Problem 3-7
		Problem 3-8
		Problem 3-9
		Problem 3-10
		Problem 3-11
		Problem 3-12
		Problem 3-13
		Problem 3-14
		Problem 3-15
		Problem 3-16
		Problem 3-17
		Problem 3-18
		Problem 3-19
		Problem 3-20
		Problem 3-21
		Problem 3-22
		Problem 3-23
		Problem 3-24
		Problem 3-25
		Problem 3-26
		Problem 3-27
		Problem 3-28
		Problem 3-29
		Problem 3-30
		Problem 3-31
		Problem 3-32
		Problem 3-33
		Problem 3-34
		Problem 3-35
		Problem 3-36
		Problem 3-37
		Problem 3-38
		Problem 3-39
		Problem 3-40
		Problem 3-41
		Problem 3-42
		Problem 3-43
		Problem 3-44
		Problem 3-45
		Problem 3-46
		Problem 3-47
		Problem 3-48
		Problem 3-49
		Problem 3-50
		Problem 3-51
		Problem 3-52
		Problem 3-53
		Problem 3-54
		Problem 3-55
		Problem 3-56
		Problem 3-57
		Problem 3-58
		Problem 3-59
		Problem 3-60
		Problem 3-61
		Problem 3-62
		Problem 3-63
		Problem 3-64
4 z-Transform
	Introduction
	4.1 The z-transform
	4.2 The singularities of H(z)
		4.2.1 Pole-zero plots
		4.2.2 Left-sided sequences
		4.2.3 Relation between the z-transform and DTFT
		4.2.4 Multiple poles and zeros
			Shifted impulse
			Right-sided sequence
			Left-sided sequence
			Double-sided convergent sequence
			Double-sided, non-convergent sequence
		4.2.5 Finding the z-transform from the pole-zero plot
		4.2.6 Complex poles and zeros
		4.2.7 Some important transforms
		4.2.8 Finite-length sequences
		4.2.9 Plotting pole-zero plots with Matlab
	4.3 Linear-phase FIR systems
		(1) Poles can only occur at the origin. Zeros can only be real or occur in complex conjugate pairs.
		(2) Zeros must occur at conjugate-reciprocal positions in the z-plane.
		(3) The product of the zeros is either +1 or -1.
		4.3.1 Complex zeros
		4.3.2 Real zeros
	4.4 The inverse z-transform
		4.4.1 All-zero systems
		4.4.2 Distinct real poles
		4.4.3 Complex poles
		4.4.4 Multiple (repeated) poles
		4.4.5 Improper rational functions
		4.4.6 Using Matlab to compute the inverse z-transform
	4.5 Properties of the z-transform
		4.5.1 Linearity
		4.5.2 Shifting property
		4.5.3 Differentiation property
		4.5.4 Time-reversal property
		4.5.5 Convolution property
		4.5.6 Applications of convolution
		4.5.7 Initial-value theorem
		4.5.8 Final-value theorem
	4.6 Linear constant-coefficient difference equations (LCCDE)
		4.6.1 LCCDE of FIR systems
		4.6.2 LCCDE of IIR systems
			Zero-input response
			Zero-state response
			Total response
		4.6.3 Relation between the LCCDE and H(z)
		4.6.4 Using Matlab to solve LCCDEs
		4.6.5 Inverse filter
	4.7 The unilateral z-transform
	Summary
	Problems
		Problem 4-1
		Problem 4-2
		Problem 4-3
		Problem 4-4
		Problem 4-5
		Problem 4-6
		Problem 4-7
		Problem 4-8
		Problem 4-9
		Problem 4-10
		Problem 4-11
		Problem 4-12
		Problem 4-13
		Problem 4-14
		Problem 4-15
		Problem 4-16
		Problem 4-17
		Problem 4-18
		Problem 4-19
		Problem 4-20
		Problem 4-21
		Problem 4-22
		Problem 4-23
		Problem 4-24
		Problem 4-25
		Problem 4-26
		Problem 4-27
		Problem 4-28
		Problem 4-29
		Problem 4-30
		Problem 4-31
		Problem 4-32
		Problem 4-33
		Problem 4-34
		Problem 4-35
		Problem 4-36
		Problem 4-37
		Problem 4-38
		Problem 4-39
		Problem 4-40
		Problem 4-41
		Problem 4-42
5 Frequency response
	Introduction
	5.1 The computation of H(ω) from H(z)
	5.2 Systems with a single real zero
		5.2.1 Direct computation
		5.2.2 Graphical method
	5.3 Systems with a single real pole
	5.4 Multiple real poles and zeros
	5.5 Complex poles and zeros
	5.6 3-D visualization of H(ω) from H(z)
	5.7 Allpass filter
		5.7.1 Real allpass filter
		5.7.2 Multiple poles and zeros
		5.7.3 Allpass filters with complex poles and zeros
		5.7.4 General allpass filter
		5.7.5 Systems with the same magnitude
		5.7.6 Practical applications of allpass filters
	5.8 Minimum-phase-lag systems
	Summary
	Problems
		Problem 5-1
		Problem 5-2
		Problem 5-3
		Problem 5-4
		Problem 5-5
		Problem 5-6
		Problem 5-7
		Problem 5-8
		Problem 5-9
		Problem 5-10
		Problem 5-11
6 A/D and D/A conversion
	Introduction
	6.1 Overview of A/D and D/A conversion
	6.2 Analog sampling and reconstruction
		6.2.1 Analog sampling
		6.2.2 The sampling theorem
			The sampling theorem in the frequency domain
			The sampling theorem in the time domain
			Reconstruction filters of different bandwidths
			Summary of the reconstruction process
		6.2.3 The Nyquist sampling criterion
		6.2.4 Oversampling, undersampling and critical sampling
			Critical sampling
			Oversampling
			Undersampling
		6.2.5 Sampling a cosine
			Oversampling
			Undersampling
			Critical sampling
	6.3 Conversion from continuous time to discrete time and back
		6.3.1 The continuous-to-discrete (C/D) converter
		6.3.2 Spectrum of the discrete-time sequence
		6.3.3 The discrete-to-continuous (D/C) converter
		6.3.4 Summary
	6.4 Anti-aliasing and reconstruction filters
		6.4.1 The anti-aliasing filter
			Ideal anti-aliasing filter
			Non-ideal anti-aliasing filter
		6.4.2 A digital recording application
		6.4.3 Reconstruction filter
		6.4.4 Revised model of D/A conversion
	6.5 Downsampling and upsampling
		6.5.1 Downsampling
			Approach 1 (bad approach):
			Approach 2 (better approach):
		6.5.2 Decimation and aliasing
		6.5.3 Oversampling A/D converter in a digital recording application
		6.5.4 Upsampling
			Approach 1 (bad approach):
			Approach 2 (better approach):
		6.5.5 Upsampling a cosine
			Linear interpolation
			Aliasing in upsampling
		6.5.6 Upsampling D/A converter in a digital recording application
			Approach I: sharp analog reconstruction filter
			Approach II: oversampling D/A converter
		6.5.7 Resampling
	6.6 Matlab functions for sample-rate conversion
		Resample
		Downsampling
		Upsampling
	6.7 Quantization
		6.7.1 Model of quantization
			Quantization
			Encoding
		6.7.2 Quantization error
		6.7.3 Noise reduction by oversampling
			Power spectral density of quantization noise
			Noise reduction in an oversampling A/D converter
		6.7.4 Noise-shaping A/D converters
			Sampling discrete-time integrator
			Analysis of noise-shaping A/D converter
		6.7.5 Sigma-delta A/D converters
	6.8 A/D converter architecture
	6.9 D/A converter architecture
	Summary
	Problems
		Problem 6-1
		Problem 6-2
		Problem 6-3
		Problem 6-4
		Problem 6-5
		Problem 6-6
		Problem 6-7
		Problem 6-8
		Problem 6-9
		Problem 6-10
		Problem 6-11
		Problem 6-12
		Problem 6-13
7 Finite impulse response filters
	Introduction
	7.1 Linear-phase FIR filters
		7.1.1 Types of linear-phase filters
		7.1.2 Basic properties of linear-phase filters
		7.1.3 Time-aligned and zero-phase FIR filters
	7.2 Preliminaries of filter design
		7.2.1 Specification of filter characteristics
		7.2.2 The ideal lowpass filter
		7.2.3 The optimum least-square-error FIR filter
		7.2.4 Even- and odd-length causal filters
	7.3 Window-based FIR filter design
		7.3.1 Rectangular window filter
			Characteristics of the rectangular-window FIR filter as a function of N and ?c
		7.3.2 Raised cosine window filters
			Hamming window
			Hann window
			Blackman window
			Comparison of raised-cosine windows
			Design formulas for window-based FIR filters
			Fractional bandwidth
		7.3.3 Kaiser window
	7.4 Highpass, bandpass and bandstop FIR filters
		Complementary filters
		Bandpass and bandstop filters
		Modulation method
	7.5 Matlab implementation of window-based FIR filters
		7.5.1 Matlab functions that implement FIR filtering
			conv
			filter
			filtfilt
	7.6 Spline and raised-cosine FIR filters
		7.6.1 FIR filters designed using splines
		7.6.2 FIR filters designed using raised cosines
	7.7 Frequency-sampled FIR filter design
		7.7.1 Inverse DFT
		7.7.2 Frequency sampling as interpolation
		7.7.3 Design formulas
		7.7.4 Simultaneous equations
		7.7.5 Matlab implementation of frequency-sampled filters
	7.8 Least-square-error FIR filter design
		7.8.1 Discrete least-square-error FIR filters
			Matrix formulation of the discrete least-square-error filter
			Discrete weighted least-square-error filter
		7.8.2 Integral least-square-error FIR filter design
	7.9 Optimal lowpass filter design
	7.10 Multiband filters
	7.11 Differentiator
	7.12 Hilbert transformer
		7.12.1 Derivation of the Hilbert transformer
		7.12.2 FIR implementation of a Hilbert transformer
		7.12.3 FFT implementation of a Hilbert transformer
		7.12.4 Applications of the Hilbert transformer
			AM demodulator
			QPSK demodulator
	Summary
	Problems
		Problem 7-1
		Problem 7-2
		Problem 7-3
		Problem 7-4
		Problem 7-5
		Problem 7-6
		Problem 7-7
		Problem 7-8
		Problem 7-9
		Problem 7-10
		Problem 7-11
		Problem 7-12
		Problem 7-13
		Problem 7-14
		Problem 7-15
		Problem 7-16
		Problem 7-17
		Problem 7-18
		Problem 7-19
		Problem 7-20
		Problem 7-21
		Problem 7-22
		Problem 7-23
		Problem 7-24
		Problem 7-25
		Problem 7-26
		Problem 7-27
		Problem 7-28
		Problem 7-29
		Problem 7-30
		Problem 7-31
		Problem 7-32
		Problem 7-33
		Problem 7-34
		Problem 7-36
		Problem 7-37
		Problem 7-38
		Problem 7-39
8 Infinite impulse response filters
	Introduction
	8.1 Definition of the IIR filter
	8.2 Overview of analog filter design
		8.2.1 Parameter definitions
			Passband
			Stopband
			Transition band
		8.2.2 Butterworth filter
			Filter definition
			Mapping passband and stopband specifications to filter parameters
			The poles of the Butterworth filter
			Normalized filter
			Second-order sections
		8.2.3 Chebyshev filter
			Chebyshev polynomials
			Mapping passband and stopband specifications to filter parameters
			The poles of the Chebyshev filter
		8.2.4 Inverse Chebyshev filter
			Mapping passband and stopband specifications to filter parameters
			The poles and zeros of the inverse Chebyshev filter
		8.2.5 Elliptic filter
			Filter definition
			The elliptic rational function
			Mapping passband and stopband specifications to filter parameters
			Poles and zeros of the elliptic filter
		8.2.6 Summary
	8.3 Impulse invariance
		8.3.1 Impulse-invariance approach
		8.3.2 Impulse-invariance design procedure
		8.3.3 Mapping of the s-plane to the z-plane
	8.4 Bilinear transformation
		8.4.1 Forward-difference approximation
		8.4.2 Backward-difference approximation
		8.4.3 Bilinear transformation
		8.4.4 Bilinear-transformation procedure
		8.4.5 Cascade of second-order sections
	8.5 Spectral transformations of IIR filters
		8.5.1 Lowpass-to-lowpass transformation
		8.5.2 Lowpass-to-highpass transformation
		8.5.3 Lowpass-to-bandpass transformation
		8.5.4 Lowpass-to-bandstop transformation
			Summary of spectral transformations
	8.6 Zero-phase IIR filtering
	Summary
	Problems
		Problem 8-1
		Problem 8-2
		Problem 8-3
		Problem 8-4
		Problem 8-5
		Problem 8-6
		Problem 8-7
		Problem 8-8
		Problem 8-9
		Problem 8-10
		Problem 8-11
		Problem 8-12
		Problem 8-13
		Problem 8-14
		Problem 8-15
		Problem 8-16
		Problem 8-17
		Problem 8-18
		Problem 8-19
		Problem 8-20
		Problem 8-21
		Problem 8-22
		Problem 8-23
		Problem 8-24
		Problem 8-25
		Problem 8-26
		Problem 8-27
		Problem 8-28
		Problem 8-29
		Problem 8-30
		Problem 8-31
		Problem 8-32
		Problem 8-33
		Problem 8-34
		Problem 8-35
		Problem 8-36
		Problem 8-37
		Problem 8-38
		Problem 8-39
		Problem 8-40
		Problem 8-41
9 Filter architecture
	Introduction
	9.1 Signal-flow graphs
	9.2 Canonical filter architecture
		9.2.1 First-order filters
			First-order FIR filter
			First-order IIR filter
		9.2.2 Canonical filter architecture
	9.3 Transposed filters
	9.4 Cascade architecture
		9.4.1 Allpass filters
		9.4.2 Using Matlab to design cascade filters
	9.5 Parallel architecture
		9.5.1 Using Matlab to design parallel filters
	9.6 FIR filters
	9.7 Lattice and lattice-ladder filters
		9.7.1 FIR lattice filters
		9.7.2 Specialized FIR lattice filters
		9.7.3 IIR lattice filters
		9.7.4 Allpass lattice filters
		9.7.5 Lattice-ladder IIR filters
		9.7.6 Stability of IIR filters revisited
	9.8 Coefficient quantization
		9.8.1 Systems with poles
		9.8.2 Systems with zeros
		9.8.3 Systems with poles and zeros
		9.8.4 Pairing poles and zeros
		9.8.5 Coefficient quantization of lattice filters
	9.9 Implementation issues
		9.9.1 Software implementation
		9.9.2 Hardware implementation
	Summary
	Problems
		Problem 9-1
		Problem 9-2
		Problem 9-3
		Problem 9-4
		Problem 9-5
		Problem 9-6
		Problem 9-7
		Problem 9-8
		Problem 9-9
		Problem 9-10
10 Discrete Fourier transform (DFT)
	Introduction
	10.1 Derivation of the DFT
		10.1.1 The inverse discrete Fourier transform (IDFT)
		10.1.2 Orthogonality of complex exponential sequences
		10.1.3 Periodicity of the DFT
		10.1.4 Conditions for the reconstruction of a sequence from the DFT
	10.2 DFT of basic signals
		10.2.1 DFT of an impulse
		10.2.2 DFT of a pulse
		10.2.3 DFT of a constant
		10.2.4 DFT of a complex exponential sequence
		10.2.5 DFT of a sinusoid
		10.2.6 Resolution and frequency mapping of the DFT
		10.2.7 summary (so far)
	10.3 Properties of the DFT
		10.3.1 Linearity
		10.3.2 Complex conjugation
		10.3.3 Symmetry properties of the DFT
			Real sequences
			General complex sequences
		10.3.4 Circular time shifting
		10.3.5 Circular time reversal
		10.3.6 Circular frequency shift
		10.3.7 Circular convolution
		10.3.8 Multiplication
		10.3.9 Parseval's theorem
		10.3.10 summary of DFT properties
	10.4 Matrix representation of the DFT
	10.5 Using the DFT to increase resolution in the time and frequency domains
		10.5.1 Increasing frequency resolution by zero-padding in the time domain
		10.5.2 Upsampling in the time domain by zero-padding in the frequency domain
		10.5.3 Recovery of the DTFT from the DFT
	Summary
	Problems
		Problem 10-1
		Problem 10-2
		Problem 10-3
		Problem 10-4
		Problem 10-5
		Problem 10-6
		Problem 10-7
		Problem 10-8
		Problem 10-9
		Problem 10-10
		Problem 10-11
		Problem 10-12
		Problem 10-13
		Problem 10-14
		Problem 10-15
		Problem 10-16
		Problem 10-17
		Problem 10-18
		Problem 10-18
		Problem 10-19
		Problem 10-20
		Problem 10-21
		Problem 10-22
		Problem 10-23
		Problem 10-24
11 Fast Fourier transform (FFT)
	Introduction
	11.1 Radix-2 FFT transforms
		11.1.1 Decimation-in-time FFT
		11.1.2 Computational gain
		11.1.3 Bit reversal
		11.1.4 Decimation-in-frequency FFT
	11.2 Radix-4 FFT
		11.2.1 The radix-4 decomposition
		11.2.2 The radix-4 transform as a combination of radix-2 transforms
	11.3 Composite (mixed-radix) FFT
		11.3.1 FFTs of composite size
		11.3.2 Mixed radix-2 and radix-4 transform
		11.3.3 Transposed and split-radix transforms
	11.4 Inverse FFT
	11.5 Matlab implementation
	11.6 FFT of real sequences
		11.6.1 Properties of DFTs (revisited)
		11.6.2 N-point FFT of two real N-point sequences
		11.6.3 N-point IFFT of two N-point transforms
		11.6.4 N/2-point FFT of a real N-point sequence
		11.6.5 N/2-point IFFT of an N-point transform
	11.7 FFT resolution
		11.7.1 Increasing the resolution of the FFT
		11.7.2 Decreasing the resolution of the FFT
	11.8 Fast convolution using the FFT
		11.8.1 Convolution of fixed-length input sequences
			Speed of convolution
		11.8.2 Block convolution using the FFT
			Overlap-add method
			Overlap-save method
			Choice of block size
		11.8.3 Using both DIT and DIF transforms
		11.8.4 Matlab support for convolution using the FFT
	11.9 The Goertzel algorithm
		DTMF tone decoding
	11.10 Iterative and recursive implementations
		11.10.1 Iterative implementation
		11.10.2 Recursive implementation
	11.11 Implementation issues
		Multiplications and additions
		Memory and cache
		Fixed-point vs. floating-point
		Hardware implementations
	Summary
	Problems
		Problem 11-1
		Problem 11-2
		Problem 11-3
		Problem 11-4
		Problem 11-5
		Problem 11-6
		Problem 11-7
		Problem 11-8
		Problem 11-9
		Problem 11-10
		Problem 11-11
		Problem 11-12
		Problem 11-13
12 Discrete cosine transform (DCT)
	Introduction
	12.1 The DCT
		12.1.1 Periodically extended sequences
		12.1.2 ''The'' discrete cosine transform (DCT-II)
		12.1.3 The inverse discrete cosine transform (IDCT)
		12.1.4 The four principal DCT variants
		12.1.5 Properties of the DCT
		12.1.6 Matrix form of the DCT and IDCT
			Parseval's theorem in matrix form
		12.1.7 Energy compaction of the DCT
		12.1.8 Implementation of the DCT-II and IDCT-II
			Computation of the DCT-II
			Computation of the IDCT-II
		12.1.9 The modified discrete cosine transform (MDCT)
	12.2 MPEG audio compression
		12.2.1 The MP3 encoder
		12.2.2 Hybrid filter bank and MDCT
		12.2.3 The psychoacoustic model
			The absolute threshold of hearing
			Critical bands
			Masking
		12.2.4 Bit allocation and quantization
		12.2.5 Minimum entropy coding
	12.3 JPEG image compression
		12.3.1 Color processing
		12.3.2 DCT transformation and quantization
		12.3.3 Coefficient encoding
		12.3.4 Implementation of 2D-DCT
	Summary
	Problems
		Problem 12-1
		Problem 12-2
		Problem 12-3
		Problem 12-4
		Problem 12-5
		Problem 12-6
		Problem 12-7
		Problem 12-8
		Problem 12-9
		Problem 12-10
		Problem 12-11
		Problem 12-12
		Problem 12-13
		Problem 12-14
		Problem 12-15
		Problem 12-16
		Problem 12-17
		Problem 12-18
		Problem 12-19
		Problem 12-20
		Problem 12-21
13 Multirate systems
	Introduction
	13.1 Polyphase downsampling
		13.1.1 Review of downsampling
		13.1.2 Polyphase implementation of downsampling
		13.1.3 Downsampling summary
	13.2 Polyphase upsampling
		13.2.1 Review of upsampling
		13.2.2 Polyphase implementation of upsampling
		13.2.3 Upsampling summary
	13.3 Polyphase resampling
	13.4 Transform analysis of polyphase systems
		13.4.1 Basic decimation and expansion identities
		13.4.2 Multirate identities of downsampling and upsampling
		z-transform of a decimated sequence
		z-transform of an expanded sequence
		Multirate downsampling identity
		Multirate upsampling identity
		13.4.3 Transform analysis of polyphase downsampling
		13.4.4 Transform analysis of polyphase upsampling
		13.4.5 Transform analysis of polyphase resampling
		13.4.6 Matlab implementation of polyphase sample-rate conversion algorithms
	13.5 Multistage systems for downsampling and upsampling
		13.5.1 Multistage downsampling
		13.5.2 Multistage upsampling
	13.6 Multistage and multirate filtering
		13.6.1 Multistage interpolated FIR (IFIR) filters
		13.6.2 Multirate lowpass filtering
	13.7 Special filters for multirate applications
		13.7.1 Half-band filters
		13.7.2 Polyphase downsampling and upsampling using half-band filters
		13.7.3 L-band (Nyquist) filters
	13.8 Multirate filter banks
	Summary
	Problems
		Problem 13-1
		Problem 13-2
		Problem 13-3
		Problem 13-4
		Problem 13-5
		Problem 13-6
		Problem 13-7
		Problem 13-8
		Problem 13-9
		Problem 13-10
		Problem 13-11
		Problem 13-12
		Problem 13-13
		Problem 13-14
		Problem 13-15
		Problem 13-16
		Problem 13-17
		Problem 13-18
		Problem 13-19
14 Spectral analysis
	Introduction
	14.1 Basics of spectral analysis
		14.1.1 Spectral effects of windowing
		14.1.2 Effect of window choice
		14.1.3 Spectral spread and leakage
			Effect of main lobe width on spectral resolution
			Effect of spectral leakage on spectral resolution
		14.1.4 Spectral effect of sampling
	14.2 The short-time Fourier transform (STFT)
		14.2.1 Constant overlap-add criterion
		14.2.2 The spectrogram
			Spectrogram of a chirp
			Spectrogram of speech
			Time resolution vs. frequency resolution of the spectrogram
		14.2.3 Implementation of the discrete STFT in Matlab
	14.3 Nonparametric methods of spectral estimation
		14.3.1 The periodogram
			Definition
			Bias of the periodogram
			Consistency of the periodogram
		14.3.2 Bartlett's method
			Periodogram of random signal in noise
		14.3.3 The modified periodogram
		14.3.4 Averaged modified periodogram
		14.3.5 Welch's method
		14.3.6 Discrete-time periodograms
		14.3.7 Matlab implementation of the periodogram functions
	14.4 Parametric methods of spectral estimation
		14.4.1 The ARMA model
			Autoregressive (AR) model
			The Yule-Walker equations
		14.4.2 The Levinson-Durbin algorithm
		14.4.3 Matlab implementation of the Levinson-Durbin algorithm
	14.5 Linear prediction
		14.5.1 Prediction error and the estimation of model order
		14.5.2 Linear predictive coding (LPC)
		14.5.3 The source-filter model
		14.5.4 Linear predictive coding architecture
			Basic LPC architecture
			Example of using linear prediction in encoding and decoding
		14.5.5 Alternative formulations of linear prediction equations
	Summary
	Problems
		Problem 14-1
		Problem 14-2
		Problem 14-3
		Problem 14-4
		Problem 14-5
		Problem 14-6
		Problem 14-7
		Problem 14-8
		Problem 14-9
A. Linear algebra
	A.1 Systems of linear equations
	A.2 Solution of an inhomogeneous system of equations
		A.2.1 Unique solution
		A.2.2 Infinite number of solutions
		A.2.3 No solution
	A.3 Solution of a homogeneous system of equations
		A.3.1 Trivial solution
		A.3.2 Infinite number of solutions
	A.4 Least-square-error optimization
B. Numeric representations
	B.1 Integer representation
		B.1.1 Unsigned binary
		B.1.2 Signed-magnitude binary
		B.1.3 Two's-complement binary
		B.1.4 Offset binary
		B.1.5 Converting between binary formats
	B.2 Fixed-point (fractional) representation
		B.2.1 Rounding and truncation
		B.2.2 Arithmetic of fractional numbers
	B.3 Floating-point representation
	B.4 Computer representation of numbers
C. Matlab tutorial
	C.1 Introduction to Matlab
		C.1.1 What is Matlab?
		C.1.2 What is Matlab not?
	C.2 The elements of Matlab
		C.2.1 Calculator functions
		C.2.2 Variables
			Variable basics
			''Reserved'' variables
			Vectors and matrices
		C.2.3 Matlab functions
			Accessing array values
			Size of matrices and arrays
			Data types
			Structures
	C.3 Programming in Matlab
		C.3.1 Scripts
		C.3.2 Functions
			Function handles
			Anonymous functions
		C.3.3 Conditionals and loops
		C.3.4 Classes
	C.4 Matlab help
	C.5 Plotting
	C.6 The Matlab environment
		C.6.1 Command window and editor
			Command window
			Editor
		C.6.2 Debugging and writing ''clean'' code
D. Probability and random processes
	D.1 Probability distribution and density functions
		D.1.1 Discrete probability density function
		D.1.2 Continuous probability density function
			Uniform PDF
			Gaussian PDF
		D.1.3 Joint, marginal and conditional probability distributions
		D.1.4 Expected value and moments
		D.1.5 Covariance and correlation
	D.2 Random processes
		D.2.1 Statistics of a random process
			Mean
			Autocorrelation
			Crosscorrelation
			Matrix form of correlation
		D.2.2 Stationary random processes
			Mean
			Autocorrelation
			Crosscorrelation
		D.2.3 White noise
		D.2.4 Filtered random processes
		D.2.5 The Wold decomposition
		D.2.6 Estimators
			Sample mean
			Sample autocorrelation
			Bias
			Consistency
		D.2.7 Ergodic processes
	D.3 Power spectral density
		D.3.1 Definition
		D.3.2 Power spectral density of a filtered random process
		D.3.3 Power spectral density of noise
	D.4 Matlab functions
		D.4.1 Random number generators
			Uniform random variables
			Gaussian random variable
			Random number generator
		D.4.2 Autocorrelation and crosscorrelation
	Problems
		Problem D1
		Problem D2
		Problem D3
		Problem D4
		Problem D5
References
	Basic linear systems theory
	DSP textbooks
	A/D and D/A conversion
	Probability and statistics
	FIR and IIR filtering
	DFT/FFT
	DCT
	Multirate systems
	Spectral analysis
Index