Signal Processing First

by McClellan, James H.; Schafer, Ronald W.; Yoder, Mark A.

• ISBN13: 9780130909992
• ISBN10: 0130909998
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-02-26
• Publisher: Pearson

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