DSP First:A Multimedia Approach

目录
1 Introduction
1.1 Mathematical Representation of Signals
1.2 Mathematical Representation of Systems
1.3 Thinking About Systems
1.4 The Next Step
2 Sinusoids
2.1 An Experiment with a Tuning Fork
2.2 Review of Sine and Cosine Functions
2.3 Sinusoidal Signals
2.3.1 Relation of Frequency to Period
2.3.2 Relation of Phase Shift to Time Shift
2.4 Sampling and Plotting Sinusoids
2.5 Complex Exponentials and Phasors
2.5.1 Review of Complex Numbers
2.5.2 Complex Exponential Signals
2.5.3 The Rotating Phasor Interpretation
2.5.4 Inverse Euler Formulas
2.6 Phasor Addition
2.6.1 Addition of Complex Numbers
2.6.2 Phasor Addition Rule
2.6.3 Phasor Addition Rule:Example
2.6.4 MATLAB Demo of Phasors
2.6.5 Summary of the Phasor Addition Rule
2.7 Physics of the Tuning Fork
2.7.1 Equations from Laws of Physics
2.7.2 General Solution to the Differential Equation
2.7.3 Listening to Tones
2.8 Time Signals:More Than Formulas
2.9 Summary and Links
Problems
3 Spectrum Representation
3.1 The Spectrum of a Sum of Sinusoids
3.1.1 Graphical Plot of the Spectrum
3.2 Beat Notes
3.2.1 Multiplication of Sinusoids
3.2.2 Beat Note Waveform
3.2.3 Amplitude Modulation
3.3 Periodic Waveforms
3.3.1 Synthetic Vowel
3.4 More Periodic Signals
3.4.1 Fourier Series:Analysis
3.4.2 The Square Wave
3.4.3 Triangle Wave
3.4.4 Example of a Non-periodic Signal
3.5 Time-Frequency Spectrum
3.5.1 Stepped Frequency
3.5.2 Spectrogram Analysis
3.6 Frequency Modulation:Chirp Signals
3.6.1 Chirp,or Linearly Swept Frequency
3.6.2 A Closer Look at Instantaneous Frequency
3.7 Summary and Links
Problems
4 Sampling and Aliasing
4.1 Sampling
4.1.1 Sampling Sinusoidal Signals
4.1.2 The Sampling Theorem
4.1.3 Aliasing
4.1.4 Folding
4.2 Spectrum View of Sampling
4.2.1 Over-Sampling
4.2.2 Aliasing Due to Under-Sampling
4.2.3 Folding Due to Under-Sampling
4.2.4 Maximum Reconstructed Frequency
4.3 Strobe Demonstration
4.3.1 Spectrum Interpretation
4.4 Discrete-to-Continuous Conversion
4.4.1 Alias Frequencies Due to Sampling
4.4.2 Interpolation with Pulses
4.4.3 Zero-Order Hold Interpolation
4.4.4 Linear Interpolation
4.4.5 Parabolic Interpolation
4.4.6 Over-Sampling Aids Interpolation
4.4.7 Ideal Bandlimited Interpolation
4.5 The Sampling Theorem
4.6 Summary and Links
Problems
5 FIR Filters
5.1 Discrete-Time Systems
5.2 The Running Average Filter
5.3 The General FIR Filter
5.3.1 An Illustration of FIR Filtering
5.3.2 The Unit Impulse Response
5.3.2.1 Unit Impulse Sequence
5.3.2.2 Unit Impulse Response Sequence
5.3.2.3 The Unit-Delay System
5.3.3 Convolution and FIR Filters
5.3.3.1 Computing the Output of a Convolution
5.3.3.2 Convolution in MATLAB
5.4 Implementation of FIR Filters
5.4.1 Building Blocks
5.4.1.1 Multiplier
5.4.1.2 Adder
5.4.1.3 Unit Delay
5.4.2 Block Diagrams
5.4.2.1 Other Block Diagrams
5.4.2.2 Internal Hardware Details
5.5 Linear Time-Invariant(LTI)Systems
5.5.1 Time Invariance
5.5.2 Linearity
5.5.3 The FIR Case
5.6 Convolution and LTI Systems
5.6.1 Derivation of the Convolution Sum
5.6.2 Some Properties of LTI Systems
5.6.2.1 Convolution as an Operator
5.6.2.2 Commutative Property of Convolution
5.6.2.3 Associative Property of Convolution
5.7 Cascaded LTI Systems
5.8 Example of FIR Filtering
5.9 Summary and Links
Problems
6 Frequency Response of FIR Filters
6.1 Sinusoidal Response of FIR Systems
6.2 Superposition and the Frequency Response
6.3 Steady State and Transient Response
6.4 Properties of the Frequency Response
6.4.1 Relation to Impulse Response and Difference Equation
6.4.2 Periodicity of〓
6.4.3 Conjugate Symmetry
6.5 Graphical Representation of the Frequency Response
6.5.1 Delay System
6.5.2 First Difference System
6.5.3 A Simple Lowpass Filter
6.6 Cascaded LTI Systems
6.7 Running-Average Filtering
6.7.1 Plotting the Frequency Response
6.7.2 Cascade of Magnitude and Phase
6.7.3 Experiment:Smoothing an Image
6.8 Filtering Sampled Continuous-Time Signals
6.8.1 Example:Low-Pass Averager
6.8.2 Interpretation of Delay
6.9 Summary and Links
Problems
7 z-Transforms
7.1 Definition of the z-Transform
7.2 The z-Transform and Linear Systems
7.2.1 The z-Transform of an FIR Filter
7.3 Properties of the z-Transform
7.3.1 The Superposition Property of the z-Transform
7.3.2 The Time-Delay Property of the z-Transform
7.3.3 A General z-Transform Formula
7.4 The z-Transform as an Operator
7.4.1 Unit-Delay Operator
7.4.2 Operator Notation
7.4.3 Operator Notation in Block Diagrams
7.5 Convolution and the z-Transform
7.5.1 Cascading Systems
7.5.2 Factoring z-Polynomials
7.5.3 Deconvolution
7.6 Relationship Between the z-Domain and the 〓-Domain
7.6.1 The z-Plane and the Unit Circle
7.6.2 The Zeros and Poles of H(z)
7.6.3 Significance of the Zeros of H(z)
7.6.4 Nulling Filters
7.6.5 Graphical Relation Between z and〓
7.7 Useful Filters
7.7.1 The L-Point Running Sum Filter
7.7.2 A Complex Bandpass Filter
7.7.3 A Bandpass Filter with Real Coefficients
7.8 Practical Bandpass Filter Design
7.9 Properties of Linear Phase Filters
7.9.1 The Linear Phase Condition
7.9.2 Locations of the Zeros of FIR Linear Phase Systems
7.10 Summary and Links
Problems
8 IIR Filters
8.1 The General IIR Difference Equation
8.2 Time-Domain Response
8.2.1 Linearity and Time Invariance of IIR Filters
8.2.2 Impulse Response of a First-Order IIR System
8.2.3 Response to Finite-Length Inputs
8.2.4 Step Response of a First-Order Recursive System
8.3 System Function of an IIR Filter
8.3.1 The General First-Order Case
8.3.2 The System Function and Block-Diagram Structures
8.3.2.1 Direct Form ⅠStructure
8.3.2.2 Direct Form ⅡStructure
8.3.2.3 The Transposed Form Structure
8.3.3 Relation to the Impulse Response
8.3.4 Summary of the Method
8.4 Poles and Zeros
8.4.1 Poles or Zeros at the Origin or Infinity
8.4.2 Pole Locations and Stability
8.5 Frequency Response of an IIR Filter
8.5.1 Frequency Response using MATLAB
8.5.2 Three-Dimensional Plot of a System Function
8.6 Three Domains
8.7 The Inverse z-Transform and Some Applications
8.7.1 Revisiting the Step Response of a First-Order System
8.7.2 A General Procedure for Inverse z-Transformation
8.8 Steady-State Response and Stability
8.9 Second-Order Filters
8.9.1 z-transform of Second-Order Filters
8.9.2 Structures for Second-Order IIR Systems
8.9.3 Poles and Zeros
8.9.4 Impulse Response of a Second-Order IIR System
8.9.4.1 Real Poles
8.9.5 Complex Poles
8.10 Frequency Response of Second-Order IIR Filter
8.10.1 Frequency Response via MATLAB
8.10.2 3-dB Bandwidth
8.10.3 Three-Dimensional Plot of System Functions
8.11 Example of an IIR Lowpass Filter
8.12 Summary and Links
Problems
9 Spectrum Analysis
9.1 Introduction and Review
9.1.1 Review of the Frequency Spectrum
9.1.2 A Spectrum Analyzer
9.2 Spectrum Analysis by Filtering
9.2.1 Frequency Shifting
9.2.2 Measuring the Average Value
9.2.3 Channel Filters
9.3 Spectrum Analysis of Periodic Signals
9.3.1 Periodic Signals
9.3.2 Spectrum of a Periodic Signal
9.3.3 Filtering with a Running Sum
9.3.4 Spectrum Analysis Using Running-Sum Filtering
9.3.5 The DFT:Discrete Fourier Transform
9.3.6 DFT Examples
9.3.7 The Fast Fourier Transform(FFT)
9.4 Spectrum Analysis of Sampled Periodic Signals
9.5 Spectrum Analysis of Nonperiodic Signals
9.5.1 Spectrum Analysis of Finite-Length Signals
9.5.2 Frequency Sampling
9.5.3 Samples of the Frequency Response
9.5.4 Spectrum Analysis of Continuing Nonperiodic Signals
9.6 The Spectrogram
9.6.1 Spectrograms in MATLAB
9.6.2 Spectrogram of a Sampled Periodic Signal
9.6.3 Resolution of the Spectrogram
9.6.3.1 Resolution Experiment
9.6.4 Spectrogram of a Musical Scale
9.6.5 Spectrogram of a Speech Signal
9.7 Filtered Speech
9.8 The Fast Fourier Transform(FFT)
9.8.1 Derivation of the FFT
9.8.1.1 FFT Operation Count
9.9 Summary and Links
Problems
Appendix A Complex Numbers
A.1 Introduction
A.2 Notation for Complex Numbers
A.2.1 Rectangular Form
A.2.2 Polar Form
A.2.3 Conversion:Rectangular and Polar
A.2.4 Difficulty in Second or Third Quadrant
A.3 Euler's Formula
A.3.1 Inverse Euler Formulas
A.4 Algebraic Rules for Complex Numbers
A.4.1 Exercises
A.5 Geometric Views of Complex Operations
A.5.1 Geometric View of Addition
A.5.2 Geometric View of Subtraction
A.5.3 Geometric View of Multiplication
A.5.4 Geometric View of Division
A.5.5 Geometric View of Inverse
A.5.6 Geometric View of Conjugate
A.6 Powers and Roots
A.6.1 Roots of Unity
A.6.1.1 Procedure for Finding Multiple Roots
A.7 Summary and Links
Problems
Appendix B Programming in MATLAB
B.1 MATLAB Help
B.2 Matrix Operations and Variables
B.2.1 The Colon Operator
B.2.2 Matrix and Array Operations
B.2.2.1 A Review of Matrix Multiplication
B.2.2.2 Pointwise Array Operations
B.3 Plots and Graphics
B.3.1 Figure Windows
B.3.2 Multiple Plots
B.3.3 Printing and Saving Graphics
B.4 Programming Constructs
B.4.1 MATLAB Built-in Functions
B.4.2 Program Flow
B.5 MATLAB Scripts
B.6 Writing a MATLAB Function
B.6.1 Creating A Clip Function
B.6.2 Debugging a MATLAB M-file
B.7 Programming Tips
B.7.1 Avoiding Loops
B.7.2 Repeating Rows or Columns
B.7.3 Vectorizing Logical Operations
B.7.4 Creating an Impulse
B.7.5 The Find Function
B.7.6 Seek to Vectorize
B.7.7 Programming Style
Appendix C Laboratory Projects
C.1 Laboratory:Introduction to MATLAB
C.1.1 Overview and Goals
C.1.2 Warm-up
C.1.2.1 Basic Commands
C.1.2.2 MATLAB Array Indexing
C.1.2.3 MATLAB Script Files
C.1.2.4 MATLAB Demos
C.1.2.5 MATLAB Sound
C.1.2.6 Functions
C.1.2.7 Vectorization
C.1.3 Exercises:Using MATLAB
C.1.3.1 Manipulating Sinusoids with MATLAB
C.1.4 Lab Review Questions
C.2 Laboratory:Introduction to Complex Exponentials
C.2.1 Overview
C.2.1.1 Complex Numbers in MATLAB
C.2.1.2 Sinusoid Addition Using Complex Exponentials
C.2.1.3 Harmonic Sinusoids
C.2.2 Warm-up
C.2.2.1 Complex Numbers
C.2.2.2 Sinusoidal Synthesis with an M-File
C.2.3 Exercises:Complex Exponentials
C.2.3.1 Representation of Sinusoids with Complex Exponentials
C.2.3.2 Verify Addition of Sinusoids Using Complex Exponentials
C.2.4 Periodic Waveforms
C.3 Laboratory:Synthesis of Sinusoidal Signals
C.3.1 Overview
C.3.2 Warm-up:Music Synthesis
C.3.2.1 D-to-A Conversion
C.3.2.2 Theory of Sampling
C.3.2.3 Piano Keyboard
C.3.3 Lab:Synthesis of Musical Notes
C.3.3.1 Spectrogram of the Music
C.3.3.2 Fur Elise
C.3.3.3 Musical Tweaks
C.3.3.4 Programming Tips
C.3.3.5 Alternative Piece:Jesu,Joy of Man's Desiring
C.3.3.6 Alternative Piece:Minuet in G
C.3.3.7 Alternative Piece:Beethoven's Fifth Symphony
C.3.3.8 Alternative Piece:Twinkle,Twinkle,Little Star
C.3.4 Sound Evaluation Criteria
C.4 Laboratory:AM and FM Sinusoidal Signals
C.4.1 Overview
C.4.1.1 Amplitude Modulation
C.4.1.2 Frequency Modulated Signals
C.4.1.3 Chirp,or Linearly Swept Frequency
C.4.1.4 Advanced Topic:Spectrograms
C.4.2 Warm-up
C.4.2.1 MATLAB Synthesis of Chirp Signals
C.4.3 Lab A:Chirps and Beats
C.4.3.1 Synthesize a Chirp
C.4.3.2 Beat Notes
C.4.3.3 More on Spectrograms(Optional)
C.4.4 Lab B:FM Synthesis of Instrument Sounds
C.4.4.1 Generating the Bell Envelopes
C.4.4.2 Parameters for the Bell
C.4.4.3 The Bell Sound
C.4.4.4 Comments about the Bell
C.4.5 Woodwinds
C.4.5.1 Generating the Envelopes for Woodwinds
C.4.5.2 Scaling the Clarinet Envelopes
C.4.5.3 Clarinet Envelopes
C.4.5.4 Parameters for the Clarinet
C.4.5.5 Experiment with the Clarinet Sound
C.5 Laboratory:FIR Filtering of Sinusoidal Waveforms
C.5.1 Overview of Filtering
C.5.1.1 Frequency Response of FIR Filters
C.5.2 Warm-up
C.5.2.1 Frequency Response of the 3-Point Averager
C.5.3 Lab:FIR Filters
C.5.3.1 Filtering Cosine Waves
C.5.3.2 First-Difference Filter
C.5.3.3 Linearity of the Filter
C.5.3.4 Time Invariance of the Filter
C.5.3.5 Cascading Two Systems
C.6 Laboratory:Filtering Sampled Waveforms
C.6.1 Overview of Linear Filters
C.6.2 Warm-up
C.6.2.1 Properties of Discrete-Time Filters
C.6.3 Laboratory:Sampling and Filters
C.6.3.1 Filtering a Stair-Step Signal
C.6.3.2 Implementation of Five-Point Averager
C.6.3.3 Implementation of First-Difference System
C.6.3.4 Implementation of First Cascade(Fig.C.11)
C.6.3.5 Implementation of Second Cascade(Fig.C.12)
C.6.3.6 Comparison of Systems of Figs.C.11 and C.12
C.6.3.7 Filtering the Speech Waveform
C.7 Laboratory:Everyday Sinusoidal Signals
C.7.1 Background
C.7.1.1 Background A:Telephone Touch Tone Dialing
C.7.1.2 DTMF Decoding
C.7.1.3 Background B:Amplitude Modulation(AM)
C.7.1.4 AM Demodulation
C.7.1.5 Envelope Detection(Peak Tracking)
C.7.1.6 LTI filter-based demodulation
C.7.1.7 Notch Filters for Demodulation
C.7.2 Warm-up A:DTMF Synthesis
C.7.2.1 DTMF Dial Function
C.7.3 Warm-up B:Tone Amplitude Modulation
C.7.4 Laboratory A:DTMF Decoding
C.7.4.1 Filter Design
C.7.4.2 A Scoring Function
C.7.4.3 DTMF Decode Function
C.7.4.4 Telephone Numbers
C.7.5 Laboratory B:AM Waveform Detection
C.7.6 Optional:Amplitude Modulation with Speech
C.8 Laboratory:Filtering and Edge Detection of Images
C.8.1 Overview
C.8.1.1 Digital Images
C.8.1.2 Displaying Images
C.8.1.3 Image Filtering
C.8.2 Warm-up:Display of Images
C.8.2.1 Display Test
C.8.3 Laboratory:Filtering Images
C.8.3.1 One-Dimensional Filtering
C.8.3.2 Blurring an Image
C.8.3.3 More Image Filters
C.8.3.4 Frequency Content of an Image
C.8.3.5 The Method of Synthetic Highs
C.8.3.6 Nonlinear Filters
C.8.3.7 Edges in an Image
C.8.3.8 The Slope-Threshold Function
C.8.3.9 What's Nonlinear about Edge Detection?
C.9 Laboratory:Sampling and Zooming of Images
C.9.1 Overview
C.9.2 Warm-up:Linear Interpolation
C.9.3 Laboratory:Sampling of Images
C.9.3.1 Reconstruction of Images
C.9.3.2 Zooming for an Image
C.10 Laboratory:The z-,n-,and 〓-Domains
C.10.1 Objective
C.10.2 Warm-up
C.10.3 Laboratory:Relationships Between z-,n-,and 〓-domains
C.10.4 Real Poles
C.10.5 Complex Poles
C.10.6 Filter Design
C.11 Laboratory:Extracting Frequencies of Musical Tones
C.11.1 Overview
C.11.2 Warm-up:System Components
C.11.2.1 Spectrogram Computation
C.11.2.2 Generating the Window
C.11.2.3 Display the Spectrogram
C.11.2.4 Finding Peaks
C.11.3 Design of the Music-Writing System
C.11.3.1 Block Diagram for the System
C.11.3.2 Write a Spectrogram Function
C.11.3.3 Parameters of the Spectrogram
C.11.3.4 Peak Picking and Editing
C.11.3.5 Writing the Musical Score
C.11.4 Testing the Music Extraction Program
Appendix D About the CD
Index