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Signal Processing First

by ; ;
Edition:
1st
ISBN13:

9780130909992

ISBN10:
0130909998
Format:
Hardcover
Pub. Date:
2/26/2003
Publisher(s):
Prentice Hall
List Price: $208.99

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Summary

This best-selling, hands-on, multimedia package provides an introduction to fundamental concepts, specifically discrete-time systems, for beginning engineering students. Created and written by the same well-respected authors, it has been adopted in over 100 institutions worldwide since publication. This class-tested learning package is also widely used as a self-teaching tool to discover more about USP applications, multimedia signals, and MATLAB reg; . Unique features such as visual learning demonstrations, MATLAB laboratories, and a bank of solved homework problems are just a few of the things that make this an essential learning tool for mastering fundamental concepts in today's electrical and computer engineering curricula.

Table of Contents

Preface xiv
Introduction
1(6)
Mathematical Representation of Signals
2(2)
Mathematical Representation of Systems
4(1)
Thinking About Systems
5(1)
The Next Step
6(1)
Sinusoids
7(29)
Tuning Fork Experiment
8(1)
Review of Sine and Cosine Functions
9(2)
Sinusoidal Signals
11(4)
Relation of Frequency to Period
12(1)
Phase Shift and Time Shift
13(2)
Sampling and Plotting Sinusoids
15(2)
Complex Exponentials and Phasors
17(5)
Review of Complex Numbers
17(1)
Complex Exponential Signals
18(1)
The Rotating Phasor Interpretation
19(2)
Inverse Euler Formulas
21(1)
Phasor Addition
22(5)
Addition of Complex Numbers
23(1)
Phasor Addition Rule
23(1)
Phasor Addition Rule: Example
24(1)
MATLAB Demo of Phasors
25(1)
Summary of the Phasor Addition Rule
26(1)
Physics of the Tuning Fork
27(2)
Equations from Laws of Physics
27(2)
General Solution to the Differential Equation
29(1)
Listening to Tones
29(1)
Time Signals: More Than Formulas
29(1)
Summary and Links
30(1)
Problems
31(5)
Spectrum Representation
36(35)
The Spectrum of a Sum of Sinusoids
36(3)
Notation Change
38(1)
Graphical Plot of the Spectrum
38(1)
Beat Notes
39(4)
Multiplication of Sinusoids
39(1)
Beat Note Waveform
40(1)
Amplitude Modulation
41(2)
Periodic Waveforms
43(4)
Synthetic Vowel
44(1)
Example of a Nonperiodic Signal
45(2)
Fourier Series
47(3)
Fourier Series: Analysis
48(1)
Fourier Series Derivation
48(2)
Spectrum of the Fourier Series
50(1)
Fourier Analysis of Periodic Signals
51(6)
The Square Wave
52(1)
DC Value of a Square Wave
53(1)
Spectrum of a Square Wave
53(1)
Synthesis of a Square Wave
54(1)
Triangle Wave
55(1)
Synthesis of a Triangle Wave
56(1)
Convergence of Fourier Synthesis
57(1)
Time--Frequency Spectrum
57(3)
Stepped Frequency
59(1)
Spectrogram Analysis
59(1)
Frequency Modulation: Chirp Signals
60(3)
Chirp or Linearly Swept Frequency
60(2)
A Closer Look at Instantaneous Frequency
62(1)
Summary and Links
63(1)
Problems
64(7)
Sampling and Aliasing
71(30)
Sampling
71(8)
Sampling Sinusoidal Signals
73(2)
The Concept of Aliasing
75(1)
Spectrum of a Discrete-Time Signal
76(1)
The Sampling Theorem
77(1)
Ideal Reconstruction
78(1)
Spectrum View of Sampling and Reconstruction
79(5)
Spectrum of a Discrete-Time Signal Obtained by Sampling
79(1)
Over-Sampling
79(2)
Aliasing Due to Under-Sampling
81(1)
Folding Due to Under-Sampling
82(1)
Maximum Reconstructed Frequency
83(1)
Strobe Demonstration
84(4)
Spectrum Interpretation
87(1)
Discrete-to-Continuous Conversion
88(5)
Interpolation with Pulses
88(1)
Zero-Order Hold Interpolation
89(1)
Linear Interpolation
90(1)
Cubic Spline Interpolation
90(1)
Over-Sampling Aids Interpolation
91(1)
Ideal Bandlimited Interpolation
92(1)
The Sampling Theorem
93(1)
Summary and Links
94(2)
Problems
96(5)
FIR Filters
101(29)
Discrete-Time Systems
102(1)
The Running-Average Filter
102(3)
The General FIR Filter
105(6)
An Illustration of FIR Filtering
106(1)
The Unit Impulse Response
107(1)
Unit Impulse Sequence
107(1)
Unit Impulse Response Sequence
108(1)
The Unit-Delay System
109(1)
Convolution and FIR Filters
110(1)
Computing the Output of a Convolution
110(1)
Convolution in MATLAB
111(1)
Implementation of FIR Filters
111(4)
Building Blocks
111(1)
Multiplier
112(1)
Adder
112(1)
Unit Delay
112(1)
Block Diagrams
113(1)
Other Block Diagrams
113(2)
Internal Hardware Details
115(1)
Linear Time-Invariant (LTI) Systems
115(3)
Time Invariance
116(1)
Linearity
117(1)
The FIR Case
117(1)
Convolution and LTI Systems
118(4)
Derivation of the Convolution Sum
118(2)
Some Properties of LTI Systems
120(1)
Convolution as an Operator
121(1)
Commutative Property of Convolution
121(1)
Associative Property of Convolution
121(1)
Cascaded LTI Systems
122(2)
Example of FIR Filtering
124(2)
Summary and Links
126(1)
Problems
126(4)
Frequency Response of FIR Filters
130(33)
Sinusoidal Response of FIR Systems
130(2)
Superposition and the Frequency Response
132(3)
Steady-State and Transient Response
135(2)
Properties of the Frequency Response
137(2)
Relation to Impulse Response and Difference Equation
137(1)
Periodicity of H(ejw)
138(1)
Conjugate Symmetry
138(1)
Graphical Representation of the Frequency Response
139(4)
Delay System
139(1)
First-Difference System
140(2)
A Simple Lowpass Filter
142(1)
Cascaded LTI Systems
143(2)
Running-Average Filtering
145(6)
Plotting the Frequency Response
146(2)
Cascade of Magnitude and Phase
148(1)
Experiment: Smoothing an Image
149(2)
Filtering Sampled Continuous-Time Signals
151(4)
Example: Lowpass Averager
152(2)
Interpretation of Delay
154(1)
Summary and Links
155(2)
Problems
157(6)
z-Transforms
163(33)
Definition of the z-Transform
164(1)
The z-Transform and Linear Systems
165(2)
The z-Transform of an FIR Filter
166(1)
Properties of the z-Transform
167(2)
The Superposition Property of the z-Transform
168(1)
The Time-Delay Property of the z-Transform
168(1)
A General z-Transform Formula
169(1)
The z-Transform as an Operator
169(2)
Unit-Delay Operator
169(1)
Operator Notation
170(1)
Operator Notation in Block Diagrams
170(1)
Convolution and the z-Transform
171(4)
Cascading Systems
173(1)
Factoring z-Polynomials
174(1)
Deconvolution
175(1)
Relationship Between the z-Domain and the w-Domain
175(6)
The z-Plane and the Unit Circle
176(1)
The Zeros and Poles of H (z)
177(1)
Significance of the Zeros of H (z)
178(1)
Nulling Filters
179(1)
Graphical Relation Between z and w
180(1)
Useful Filters
181(5)
The L-Point Running-Sum Filter
181(2)
A Complex Bandpass Filter
183(2)
A Bandpass Filter with Real Coefficients
185(1)
Practical Bandpass Filter Design
186(3)
Properties of Linear-Phase Filters
189(1)
The Linear-Phase Condition
189(1)
Locations of the Zeros of FIR Linear-Phase Systems
189(1)
Summary and Links
190(1)
Problems
191(5)
IIR Filters
196(49)
The General IIR Difference Equation
197(1)
Time-Domain Response
198(6)
Linearity and Time Invariance of IIR Filters
199(1)
Impulse Response of a First-Order IIR System
200(1)
Response to Finite-Length Inputs
201(1)
Step Response of a First-Order Recursive System
202(2)
System Function of an IIR Filter
204(6)
The General First-Order Case
205(1)
The System Function and Block-Diagram Structures
206(1)
Direct Form I Structure
206(1)
Direct Form II Structure
207(1)
The Transposed Form Structure
208(1)
Relation to the Impulse Response
209(1)
Summary of the Method
209(1)
Poles and Zeros
210(2)
Poles or Zeros at the Origin or Infinity
211(1)
Pole Locations and Stability
211(1)
Frequency Response of an IIR Filter
212(4)
Frequency Response using MATLAB
213(1)
Three-Dimensional Plot of a System Function
214(2)
Three Domains
216(1)
The Inverse z-Transform and Some Applications
216(4)
Revisiting the Step Response of a First-Order System
217(1)
A General Procedure for Inverse z-Transformation
218(2)
Steady-State Response and Stability
220(3)
Second-Order Filters
223(8)
z-Transform of Second-Order Filters
223(1)
Structures for Second-Order IIR Systems
224(1)
Poles and Zeros
225(1)
Impulse Response of a Second-Order IIR System
226(1)
Real Poles
227(1)
Complex Poles
228(3)
Frequency Response of Second-Order IIR Filter
231(5)
Frequency Response via MATLAB
232(1)
3-dB Bandwidth
232(1)
Three-Dimensional Plot of System Functions
233(3)
Example of an IIR Lowpass Filter
236(1)
Summary and Links
237(1)
Problems
238(7)
Continuous-Time Signals and LTI Systems
245(40)
Continuous-Time Signals
246(2)
Two-Sided Infinite-Length Signals
246(1)
One-Sided Signals
247(1)
Finite-Length Signals
248(1)
The Unit Impulse
248(6)
Sampling Property of the Impulse
250(2)
Mathematical Rigor
252(1)
Engineering Reality
252(1)
Derivative of the Unit Step
252(2)
Continuous-Time Systems
254(1)
Some Basic Continuous-Time Systems
254(1)
Continuous-Time Outputs
255(1)
Analogous Discrete-Time Systems
255(1)
Linear Time-Invariant Systems
255(5)
Time-Invariance
256(1)
Linearity
256(1)
The Convolution Integral
257(2)
Properties of Convolution
259(1)
Impulse Responses of Basic LTI Systems
260(1)
Integrator
260(1)
Differentiator
261(1)
Ideal Delay
261(1)
Convolution of Impulses
261(2)
Evaluating Convolution Integrals
263(7)
Delayed Unit-Step Input
263(4)
Evaluation of Discrete Convolution
267(1)
Square-Pulse Input
268(1)
Very Narrow Square Pulse Input
269(1)
Discussion of Convolution Examples
270(1)
Properties of LTI Systems
270(6)
Cascade and Parallel Combinations
270(2)
Differentiation and Integration of Convolution
272(1)
Stability and Causality
273(3)
Using Convolution to Remove Multipath Distortion
276(2)
Summary
278(1)
Problems
279(6)
Frequency Response
285(22)
The Frequency Response Function for LTI Systems
285(4)
Plotting the Frequency Response
287(1)
Logarithmic Plot
288(1)
Magnitude and Phase Changes
288(1)
Response to Real Sinusoidal Signals
289(6)
Cosine Inputs
290(1)
Symmetry of H (jw)
290(3)
Response to a General Sum of Sinusoids
293(1)
Periodic Input Signals
294(1)
Ideal Filters
295(3)
Ideal Delay System
295(1)
Ideal Lowpass Filter
296(1)
Ideal Highpass Filter
297(1)
Ideal Bandpass Filter
297(1)
Application of Ideal Filters
298(2)
Time-Domain or Frequency-Domain?
300(1)
Summary/Future
301(1)
Problems
302(5)
Continuous-Time Fourier Transform
307(39)
Definition of the Fourier Transform
308(2)
Fourier Transform and the Spectrum
310(2)
Limit of the Fourier Series
310(2)
Existence and Convergence of the Fourier Transform
312(1)
Examples of Fourier Transform Pairs
313(9)
Right-Sided Real Exponential Signals
313(1)
Bandwidth and Decay Rate
314(1)
Rectangular Pulse Signals
314(2)
Bandlimited Signals
316(1)
Impulse in Time or Frequency
317(1)
Sinusoids
318(1)
Periodic Signals
319(3)
Properties of Fourier Transform Pairs
322(4)
The Scaling Property
322(2)
Symmetry Properties of Fourier Transform Pairs
324(2)
The Convolution Property
326(6)
Frequency Response
326(1)
Fourier Transform of a Convolution
327(1)
Examples of the Use of the Convolution Property
328(1)
Convolution of Two Bandlimited Functions
328(1)
Product of Two Sinc Functions
329(1)
Partial Fraction Expansions
330(2)
Basic LTI Systems
332(3)
Time Delay
332(1)
Differentiation
333(1)
Systems Described by Differential Equations
334(1)
The Multiplication Property
335(2)
The General Signal Multiplication Property
335(1)
The Frequency Shifting Property
336(1)
Table of Fourier Transform Properties and Pairs
337(1)
Using the Fourier Transform for Multipath Analysis
337(4)
Summary
341(1)
Problems
342(4)
Filtering, Modulation, and Sampling
346(43)
Linear Time-Invariant Systems
346(12)
Cascade and Parallel Configurations
347(1)
Ideal Delay
348(3)
Frequency Selective Filters
351(1)
Ideal Lowpass Filter
351(1)
Other Ideal Frequency Selective Filters
352(1)
Example of Filtering in the Frequency-Domain
353(2)
Compensation for the Effect of an LTI Filter
355(3)
Sinewave Amplitude Modulation
358(10)
Double-Sideband Amplitude Modulation
358(4)
DSBAM with Transmitted Carrier (DSBAM-TC)
362(4)
Frequency Division Multiplexing
366(2)
Sampling and Reconstruction
368(12)
The Sampling Theorem and Aliasing
368(2)
Bandlimited Signal Reconstruction
370(2)
Bandlimited Interpolation
372(1)
Ideal C-to-D and D-to-C Converters
373(2)
The Discrete-Time Fourier Transform
375(1)
The Inverse DTFT
376(1)
Discrete-Time Filtering of Continuous-Time Signals
377(3)
Summary
380(1)
Problems
381(8)
Computing the Spectrum
389(38)
Finite Fourier Sum
390(1)
Too Many Fourier Transforms?
391(2)
Relation of the DTFT to the CTFT
392(1)
Relation of the DFT to the DTFT
393(1)
Relation of the DFT to the CTFT
393(1)
Time-Windowing
393(2)
Analysis of a Sum of Sinusoids
395(4)
DTFT of a Windowed Sinusoid
398(1)
Discrete Fourier Transform
399(6)
The Inverse DFT
400(1)
Summary of the DFT Representation
401(1)
The Fast Fourier Transform (FFT)
402(1)
Negative Frequencies and the DFT
402(1)
DFT Example
403(2)
Spectrum Analysis of Finite-Length Signals
405(2)
Spectrum Analysis of Periodic Signals
407(1)
The Spectrogram
408(12)
Spectrogram Display
409(1)
Spectrograms in MATLAB
410(1)
Spectrogram of a Sampled Periodic Signal
410(1)
Resolution of the Spectrogram
411(1)
Resolution Experiment
412(1)
Spectrogram of a Musical Scale
413(2)
Spectrogram of a Speech Signal
415(3)
Filtered Speech
418(2)
The Fast Fourier Transform (FFT)
420(3)
Derivation of the FFT
420(1)
FFT Operation Count
421(2)
Summary and Links
423(1)
Problems
424(3)
A Complex Numbers
427(16)
Introduction
428(1)
Notation for Complex Numbers
428(3)
Rectangular Form
428(1)
Polar Form
429(1)
Conversion: Rectangular and Polar
430(1)
Difficulty in Second or Third Quadrant
431(1)
Euler's Formula
431(1)
Inverse Euler Formulas
432(1)
Algebraic Rules for Complex Numbers
432(2)
Complex Number Exercises
434(1)
Geometric Views of Complex Operations
434(4)
Geometric View of Addition
435(1)
Geometric View of Subtraction
436(1)
Geometric View of Multiplication
437(1)
Geometric View of Division
437(1)
Geometric View of the Inverse, z-1
437(1)
Geometric View of the Conjugate, z*
438(1)
Powers and Roots
438(3)
Roots of Unity
439(1)
Procedure for Finding Multiple Roots
440(1)
Summary and Links
441(1)
Problems
441(2)
B Programming in MATLAB
443(12)
MATLAB Help
444(1)
Matrix Operations and Variables
444(2)
The Colon Operator
445(1)
Matrix and Array Operations
445(1)
A Review of Matrix Multiplication
445(1)
Pointwise Array Operations
446(1)
Plots and Graphics
446(1)
Figure Windows
447(1)
Multiple Plots
447(1)
Printing and Saving Graphics
447(1)
Programming Constructs
447(1)
MATLAB Built-in Functions
448(1)
Program Flow
448(1)
MATLAB Scripts
448(1)
Writing a MATLAB Function
448(3)
Creating A Clip Function
449(2)
Debugging a MATLAB M-file
451(1)
Programming Tips
451(4)
Avoiding Loops
452(1)
Repeating Rows or Columns
452(1)
Vectorizing Logical Operations
452(1)
Creating an Impulse
453(1)
The Find Function
453(1)
Seek to Vectorize
454(1)
Programming Style
454(1)
C Laboratory Projects
455(23)
Introduction to MATLAB
457(6)
Pre-Lab
457(1)
Overview
457(1)
Movies: MATLAB Tutorials
457(1)
Getting Started
458(1)
Warm-up
458(1)
MATLAB Array Indexing
459(1)
MATLAB Script Files
459(1)
MATLAB Sound (optional)
460(1)
Laboratory: Manipulating Sinusoids with MATLAB
460(1)
Theoretical Calculations
461(1)
Complex Amplitude
461(1)
Lab Review Questions
461(2)
Encoding and Decoding Touch-Tone Signals
463(10)
Introduction
463(1)
Review
463(1)
Background: Telephone Touch-Tone Dialing
463(1)
DTMF Decoding
464(1)
Pre-Lab
464(1)
Signal Concatenation
464(1)
Comment on Efficiency
465(1)
Encoding from a Table
465(1)
Overlay Plotting
465(1)
Warm-up: DTMF Synthesis
465(1)
DTMF Dial Function
466(1)
Simple Bandpass Filter Design
467(1)
Lab: DTMF Decoding
468(1)
Filter Bank Design: dtmfdesign.m
468(1)
A Scoring Function: dtmfscore.m
469(1)
DTMF Decode Function: dtmfrun.m
470(1)
Testing
471(1)
Telephone Numbers
471(1)
Demo
472(1)
Two Convolution GUIs
473(5)
Introduction
473(1)
Pre-Lab: Run the GUIs
473(1)
Discrete-Time Convolution Demo
473(1)
Continuous-Time Convolution Demo
474(1)
Warm-up: Run the GUIs
475(1)
Continuous-Time Convolution GUI
475(1)
Discrete Convolution GUI
475(1)
Lab Exercises
475(1)
Continuous-Time Convolution
475(1)
Continuous-Time Convolution Again
476(1)
Discrete-Time Convolution
476(2)
D CD-ROM Demos
478(4)
Index 482

Excerpts

This book and its accompanying CD-ROM are the result of almost 10 years of work that originated from, and was guided by, the premise that signal processing is the best starting point for the study of both electrical engineering and computer engineering. In the summer of 1993, two of us (J. H. McC and R. W. S) began to develop a one-quarter course that was to become the first course for Georgia Tech computer engineering students, who were at that time following an overlapping, but separate, curriculum track from the electrical engineering students in the School of ECE. We argued that the subject of digital signal processing (DSP) had everything we wanted in a first course for computer engineers: it introduced the students to the use of mathematics as a language for thinking about engineering problems; it laid useful groundwork for subsequent courses; it made a strong connection to digital computation as a means for implementing systems; and it offered the possibility of interesting applications to motivate beginning engineers to do the hard work of connecting mathematics and computation to problem solving. We were not the first to have this idea. In particular, two books by Professor Ken Steiglitz of Princeton University had a major impact on our thinking. The major reasons that it was feasible in 1993 to experiment with what came to be known at Georgia Tech as the "DSP First" approach were: (1) the easy accessibility of increasingly powerful personal computers and (2) the availability of MATLAB, a powerful and easy-to-use software environment for numerical computation. Indeed, Steiglitz's 1972 book was well ahead of its time, since DSP had few practical applications, and even simple simulations on then-available batch processing computers required significant programming effort. By the early 1990s, however, DSP applications such as CD audio, high-speed modems, and cell phones were widespread due to the availability of lowcost "DSP chips" that could perform extensive computation in "real time:" Thus, integrated circuit technology was the driving force that simultaneously provided the wherewithal both for a convenient PC-based laboratory experience for learning DSP and for creating a climate of applications that provided motivation for that study. From the beginning, we believed that "hands-on" experience with real signals was crucial. This is provided by a "laboratory" based on MATLAB running on PCs. In the laboratory assignments, students gain direct reinforcement from hearing and seeing the effects of filtering operations that they have implemented on sound and image signals. They synthesize music from sinusoids, and they see that those same sinusoids are the basis for the data modems that they use routinely to access the Internet. We also found that MATLAB made it possible to quickly develop demonstration programs for visualizing and clarifying complicated mathematical concepts. By 1995, we had written notes covering the topics in our course, and we had amassed a large amount of computer-based supporting material. Mark Yoder, while on sabbatical leave from Rose-Hulman, had the idea to put all of this material in a form that other teachers (and students) could access easily. That idea led to a CDROM that captured the entire contents of our course web site. It included demonstrations and animations used in classes, laboratory assignments, and solved homework problems. As teachers, this material has changed the way we present ideas, because it offers new ways to visualize a concept "beyond the equations:" Over the years, our web site has continued to grow. We anticipate that this growth will continue, and that users of this material will see new ideas take shape in the form of additional demos and labs. In 1998, all of this material was packaged together in a textbook/CD-ROM, and we gave it the descriptive titleDSP First: A Multimedia Approach. No sooner had we finished DSP First, then Georgia Tech s


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