DSP First A Multimedia Approach

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

• ISBN13: 9780132431712
• ISBN10: 0132431718
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-12-30
• Publisher: Prentice Hall

Summary

This hands on, multi-media package provides a motivating introduction to fundamental concepts, specifically discrete-time systems, for beginning engineering readers. This class-tested learning package can also be used as a self-teaching tool for anyone eager to discover more about DSP applications, multi-media signals, and MATLAB.Presents basic DSP concepts in a clear and intuitive style. Integrated laboratory projects related to music, sound and image processing and new MATLAB functions for basic DSP operations are also included.Appropriate for readers interested in mastering fundamental concepts in today's electrical and computer engineering curriculum.

Table of Contents

Preface	xvii
1 Introduction	1	(8)
1.1 Mathematical Representation of Signals	2	(3)
1.2 Mathematical Representation of Systems	5	(2)
1.3 Thinking About Systems	7	(1)
1.4 The Next Step	8	(1)
2 Sinusoids	9	(39)
2.1 An Experiment with a Tuning Fork	10	(2)
2.2 Review of Sine and Cosine Functions	12	(3)
2.3 Sinusoidal Signals	15	(5)
2.3.1 Relation of Frequency to Period	16	(1)
2.3.2 Relation of Phase Shift to Time Shift	17	(3)
2.4 Sampling and Plotting Sinusoids	20	(3)
2.5 Complex Exponentials and Phasors	23	(8)
2.5.1 Review of Complex Numbers	23	(2)
2.5.2 Complex Exponential Signals	25	(1)
2.5.3 The Rotating Phasor Interpretation	26	(3)
2.5.4 Inverse Euler Formulas	29	(2)
2.6 Phasor Addition	31	(6)
2.6.1 Addition of Complex Numbers	32	(1)
2.6.2 Phasor Addition Rule	32	(2)
2.6.3 Phasor Addition Rule: Example	34	(1)
2.6.4 MATLAB Demo of Phasors	35	(1)
2.6.5 Summary of the Phasor Addition Rule	36	(1)
2.7 Physics of the Tuning Fork	37	(4)
2.7.1 Equations from Laws of Physics	37	(3)
2.7.2 General Solution to the Differential Equation	40	(1)
2.7.3 Listening to Tones	41	(1)
2.8 Time Signals: More Than Formulas	41	(1)
2.9 Summary and Links	42	(1)
Problems	43	(5)
3 Spectrum Representation	48	(35)
3.1 The Spectrum of a Sum of Sinusoids	48	(3)
3.1.1 Graphical Plot of the Spectrum	50	(1)
3.2 Beat Notes	51	(6)
3.2.1 Multiplication of Sinusoids	52	(1)
3.2.2 Beat Note Waveform	52	(2)
3.2.3 Amplitude Modulation	54	(3)
3.3 Periodic Waveforms	57	(5)
3.3.1 Synthetic Vowel	58	(4)
3.4 More Periodic Signals	62	(6)
3.4.1 Fourier Series: Analysis	62	(1)
3.4.2 The Square Wave	63	(1)
3.4.3 Triangle Wave	64	(1)
3.4.4 Example of a Non-periodic Signal	65	(3)
3.5 Time-Frequency Spectrum	68	(5)
3.5.1 Stepped Frequency	71	(1)
3.5.2 Spectrogram Analysis	72	(1)
3.6 Frequency Modulation: Chirp Signals	73	(4)
3.6.1 Chirp, or Linearly Swept Frequency	73	(2)
3.6.2 A Closer Look at Instantaneous Frequency	75	(2)
3.7 Summary and Links	77	(1)
Problems	78	(5)
4 Sampling and Aliasing	83	(36)
4.1 Sampling	83	(7)
4.1.1 Sampling Sinusoidal Signals	85	(2)
4.1.2 The Sampling Theorem	87	(1)
4.1.3 Aliasing	88	(1)
4.1.4 Folding	89	(1)
4.2 Spectrum View of Sampling	90	(4)
4.2.1 Over-Sampling	90	(2)
4.2.2 Aliasing Due to Under-Sampling	92	(1)
4.2.3 Folding Due to Under-Sampling	93	(1)
4.2.4 Maximum Reconstructed Frequency	94	(1)
4.3 Strobe Demonstration	94	(6)
4.3.1 Spectrum Interpretation	99	(1)
4.4 Discrete-to-Continuous Conversion	100	(9)
4.4.1 Alias Frequencies Due to Sampling	101	(1)
4.4.2 Interpolation with Pulses	102	(1)
4.4.3 Zero-Order Hold Interpolation	103	(1)
4.4.4 Linear Interpolation	104	(1)
4.4.5 Parabolic Interpolation	105	(1)
4.4.6 Over-Sampling Aids Interpolation	106	(1)
4.4.7 Ideal Bandlimited Interpolation	107	(2)
4.5 The Sampling Theorem	109	(2)
4.6 Summary and Links	111	(1)
Problems	112	(7)
5 FIR Filters	119	(38)
5.1 Discrete-Time Systems	119	(2)
5.2 The Running Average Filter	121	(3)
5.3 The General FIR Filter	124	(9)
5.3.1 An Illustration of FIR Filtering	125	(2)
5.3.2 The Unit Impulse Response	127	(4)
5.3.2.1 Unit Impulse Sequence	128	(1)
5.3.2.2 Unit Impulse Response Sequence	129	(1)
5.3.2.3 The Unit-Delay System	130	(1)
5.3.3 Convolution and FIR Filters	131	(2)
5.3.3.1 Computing the Output of a Convolution	131	(2)
5.3.3.2 Convolution in MATLAB	133	(1)
5.4 Implementation of FIR Filters	133	(5)
5.4.1 Building Blocks	134	(1)
5.4.1.1 Multiplier	134	(1)
5.4.1.2 Adder	134	(1)
5.4.1.3 Unit Delay	135	(1)
5.4.2 Block Diagrams	135	(3)
5.4.2.1 Other Block Diagrams	136	(1)
5.4.2.2 Internal Hardware Details	137	(1)
5.5 Linear Time-Invariant (LTI) Systems	138	(4)
5.5.1 Time Invariance	139	(1)
5.5.2 Linearity	140	(1)
5.5.3 The FIR Case	141	(1)
5.6 Convolution and LTI Systems	142	(4)
5.6.1 Derivation of the Convolution Sum	142	(2)
5.6.2 Some Properties of LTI Systems	144	(2)
5.6.2.1 Convolution as an Operator	144	(1)
5.6.2.2 Commutative Property of Convolution	145	(1)
5.6.2.3 Associative Property of Convolution	146	(1)
5.7 Cascaded LTI Systems	146	(3)
5.8 Example of FIR Filtering	149	(3)
5.9 Summary and Links	152	(1)
Problems	152	(5)
6 Frequency Response of FIR Filters	157	(45)
6.1 Sinusoidal Response of FIR Systems	157	(3)
6.2 Superposition and the Frequency Response	160	(4)
6.3 Steady State and Transient Response	164	(2)
6.4 Properties of the Frequency Response	166	(3)
6.4.1 Relation to Impulse Response and Difference Equation	166	(2)
6.4.2 Periodicity of H (w)	168	(1)
6.4.3 Conjugate Symmetry	168	(1)
6.5 Graphical Representation of the Frequency Response	169	(7)
6.5.1 Delay System	170	(1)
6.5.2 First Difference System	170	(4)
6.5.3 A Simple Lowpass Filter	174	(2)
6.6 Cascaded LTI Systems	176	(3)
6.7 Running-Average Filtering	179	(9)
6.7.1 Plotting the Frequency Response	180	(4)
6.7.2 Cascade of Magnitude and Phase	184	(1)
6.7.3 Experiment: Smoothing an Image	184	(4)
6.8 Filtering Sampled Continuous-Time Signals	188	(6)
6.8.1 Example: Low-Pass Averager	190	(2)
6.8.2 Interpretation of Delay	192	(2)
6.9 Summary and Links	194	(1)
Problems	195	(7)
7 z-Transforms	202	(47)
7.1 Definition of the z-Transform	203	(2)
7.2 The z-Transform and Linear Systems	205	(3)
7.2.1 The z-Transform of an FIR Filter	205	(3)
7.3 Properties of the z-Transform	208	(3)
7.3.1 The Superposition Property of the z-Transform	208	(1)
7.3.2 The Time-Delay Property of the z-Transform	209	(1)
7.3.3 A General z-Transform Formula	210	(1)
7.4 The z-Transform as an Operator	211	(2)
7.4.1 Unit-Delay Operator	211	(1)
7.4.2 Operator Notation	212	(1)
7.4.3 Operator Notation in Block Diagrams	213	(1)
7.5 Convolution and the z-Transform	213	(7)
7.5.1 Cascading Systems	217	(1)
7.5.2 Factoring z-Polynomials	218	(1)
7.5.3 Deconvolution	219	(1)
7.6 Relationship Between the z-Domain and the w-Domain	220	(8)
7.6.1 The z-Plane and the Unit Circle	221	(1)
7.6.2 The Zeros and Poles of H(z)	222	(2)
7.6.3 Significance of the Zeros of H(z)	224	(1)
7.6.4 Nulling Filters	225	(1)
7.6.5 Graphical Relation Between z and w	226	(2)
7.7 Useful Filters	228	(8)
7.7.1 The L-Point Running Sum Filter	229	(2)
7.7.2 A Complex Bandpass Filter	231	(3)
7.7.3 A Bandpass Filter with Real Coefficients	234	(2)
7.8 Practical Bandpass Filter Design	236	(3)
7.9 Properties of Linear Phase Filters	239	(3)
7.9.1 The Linear Phase Condition	239	(2)
7.9.2 Locations of the Zeros of FIR Linear Phase Systems	241	(1)
7.10 Summary and Links	242	(1)
Problems	242	(7)
8 IIR Filters	249	(71)
8.1 The General IIR Difference Equation	250	(1)
8.2 Time-Domain Response	251	(10)
8.2.1 Linearity and Time Invariance of IIR Filters	254	(1)
8.2.2 Impulse Response of a First-Order IIR System	254	(2)
8.2.3 Response to Finite-Length Inputs	256	(2)
8.2.4 Step Response of a First-Order Recursive System	258	(3)
8.3 System Function of an IIR Filter	261	(8)
8.3.1 The General First-Order Case	261	(2)
8.3.2 The System Function and Block-Diagram Structures	263	(4)
8.3.2.1 Direct Form I Structure	263	(1)
8.3.2.2 Direct Form II Structure	264	(1)
8.3.2.3 The Transposed Form Structure	265	(2)
8.3.3 Relation to the Impulse Response	267	(1)
8.3.4 Summary of the Method	268	(1)
8.4 Poles and Zeros	269	(3)
8.4.1 Poles or Zeros at the Origin or Infinity	270	(1)
8.4.2 Pole Locations and Stability	271	(1)
8.5 Frequency Response of an IIR Filter	272	(6)
8.5.1 Frequency Response using MATLAB	274	(2)
8.5.2 Three-Dimensional Plot of a System Function	276	(2)
8.6 Three Domains	278	(1)
8.7 The Inverse z-Transform and Some Applications	279	(6)
8.7.1 Revisiting the Step Response of a First-Order System	280	(2)
8.7.2 A General Procedure for Inverse z-Transformation	282	(3)
8.8 Steady-State Response and Stability	285	(4)
8.9 Second-Order Filters	289	(13)
8.9.1 z-transform of Second-Order Filters	289	(2)
8.9.2 Structures for Second-Order IIR Systems	291	(2)
8.9.3 Poles and Zeros	293	(2)
8.9.4 Impulse Response of a Second-Order IIR System	295	(2)
8.9.4.1 Real Poles	296	(1)
8.9.5 Complex Poles	297	(5)
8.10 Frequency Response of Second-Order IIR Filter	302	(5)
8.10.1 Frequency Response via MATLAB	303	(2)
8.10.2 3-dB Bandwidth	305	(1)
8.10.3 Three-Dimensional Plot of System Functions	305	(2)
8.11 Example of an IIR Lowpass Filter	307	(3)
8.12 Summary and Links	310	(1)
Problems	311	(9)
9 Spectrum Analysis	320	(58)
9.1 Introduction and Review	321	(3)
9.1.1 Review of the Frequency Spectrum	321	(1)
9.1.2 A Spectrum Analyzer	322	(2)
9.2 Spectrum Analysis by Filtering	324	(4)
9.2.1 Frequency Shifting	324	(1)
9.2.2 Measuring the Average Value	325	(1)
9.2.3 Channel Filters	325	(3)
9.3 Spectrum Analysis of Periodic Signals	328	(12)
9.3.1 Periodic Signals	328	(1)
9.3.2 Spectrum of a Periodic Signal	329	(2)
9.3.3 Filtering with a Running Sum	331	(1)
9.3.4 Spectrum Analysis Using Running-Sum Filtering	331	(3)
9.3.5 The DFT: Discrete Fourier Transform	334	(2)
9.3.6 DFT Examples	336	(2)
9.3.7 The Fast Fourier Transform (FFT)	338	(2)
9.4 Spectrum Analysis of Sampled Periodic Signals	340	(3)
9.5 Spectrum Analysis of Nonperiodic Signals	343	(12)
9.5.1 Spectrum Analysis of Finite-Length Signals	344	(3)
9.5.2 Frequency Sampling	347	(2)
9.5.3 Samples of the Frequency Response	349	(2)
9.5.4 Spectrum Analysis of Continuing Nonperiodic Signals	351	(4)
9.6 The Spectrogram	355	(13)
9.6.1 Spectrograms in MATLAB	356	(1)
9.6.2 Spectrogram of a Sampled Periodic Signal	357	(2)
9.6.3 Resolution of the Spectrogram	359	(2)
9.6.3.1 Resolution Experiment	360	(1)
9.6.4 Spectrogram of a Musical Scale	361	(2)
9.6.5 Spectrogram of a Speech Signal	363	(5)
9.7 Filtered Speech	368	(3)
9.8 The Fast Fourier Transform (FFT)	371	(3)
9.8.1 Derivation of the FFT	371	(3)
9.8.1.1 FFT Operation Count	373	(1)
9.9 Summary and Links	374	(2)
Problems	376	(2)
Appendix A Complex Numbers	378	(21)
A.1 Introduction	379	(1)
A.2 Notation for Complex Numbers	380	(4)
A.2.1 Rectangular Form	380	(1)
A.2.2 Polar Form	381	(1)
A.2.3 Conversion: Rectangular and Polar	381	(2)
A.2.4 Difficulty in Second or Third Quadrant	383	(1)
A.3 Euler's Formula	384	(1)
A.3.1 Inverse Euler Formulas	385	(1)
A.4 Algebraic Rules for Complex Numbers	385	(3)
A.4.1 Exercises	388	(1)
A.5 Geometric Views of Complex Operations	388	(5)
A.5.1 Geometric View of Addition	389	(1)
A.5.2 Geometric View of Subtraction	390	(1)
A.5.3 Geometric View of Multiplication	391	(1)
A.5.4 Geometric View of Division	391	(1)
A.5.5 Geometric View of Inverse	392	(1)
A.5.6 Geometric View of Conjugate	393	(1)
A.6 Powers and Roots	393	(4)
A.6.1 Roots of Unity	394	(3)
A.6.1.1 Procedure for Finding Multiple Roots	395	(2)
A.7 Summary and Links	397	(1)
Problems	398	(1)
Appendix B Programming in MATLAB	399	(16)
B.1 MATLAB Help	400	(1)
B.2 Matrix Operations and Variables	400	(3)
B.2.1 The Colon Operator	401	(1)
B.2.2 Matrix and Array Operations	401	(2)
B.2.2.1 A Review of Matrix Multiplication	402	(1)
B.2.2.2 Pointwise Array Operations	403	(1)
B.3 Plots and Graphics	403	(2)
B.3.1 Figure Windows	404	(1)
B.3.2 Multiple Plots	404	(1)
B.3.3 Printing and Saving Graphics	405	(1)
B.4 Programming Constructs	405	(1)
B.4.1 MATLAB Built-in Functions	406	(1)
B.4.2 Program Flow	406	(1)
B.5 MATLAB Scripts	406	(1)
B.6 Writing a MATLAB Function	407	(3)
B.6.1 Creating A Clip Function	408	(2)
B.6.2 Debugging a MATLAB M-file	410	(1)
B.7 Programming Tips	410	(5)
B.7.1 Avoiding Loops	411	(1)
B.7.2 Repeating Rows or Columns	411	(1)
B.7.3 Vectorizing Logical Operations	412	(1)
B.7.4 Creating an Impulse	413	(1)
B.7.5 The Find Function	413	(1)
B.7.6 Seek to Vectorize	414	(1)
B.7.7 Programming Style	414	(1)
Appendix C Laboratory Projects	415	(93)
C.1 Laboratory: Introduction to MATLAB	417	(10)
C.1.1 Overview and Goals	417	(1)
C.1.2 Warm-up	417	(6)
C.1.2.1 Basic Commands	417	(2)
C.1.2.2 MATLAB Array Indexing	419	(1)
C.1.2.3 MATLAB Script Files	419	(1)
C.1.2.4 MATLAB Demos	420	(1)
C.1.2.5 MATLAB Sound	421	(1)
C.1.2.6 Functions	421	(2)
C.1.2.7 Vectorization	423	(1)
C.1.3 Exercises: Using MATLAB	423	(1)
C.1.3.1 Manipulating Sinusoids with MATLAB	424	(1)
C.1.4 Lab Review Questions	424	(3)
C.2 Laboratory: Introduction to Complex Exponentials	427	(6)
C.2.1 Overview	427	(2)
C.2.1.1 Complex Numbers in MATLAB	427	(1)
C.2.1.2 Sinusoid Addition Using Complex Exponentials	428	(1)
C.2.1.3 Harmonic Sinusoids	429	(1)
C.2.2 Warm-up	429	(1)
C.2.2.1 Complex Numbers	429	(1)
C.2.2.2 Sinusoidal Synthesis with an M-File	429	(1)
C.2.3 Exercises: Complex Exponentials	430	(2)
C.2.3.1 Representation of Sinusoids with Complex Exponentials	430	(1)
C.2.3.2 Verify Addition of Sinusoids Using Complex Exponentials	431	(1)
C.2.4 Periodic Waveforms	432	(1)
C.3 Laboratory: Synthesis of Sinusoidal Signals	433	(10)
C.3.1 Overview	433	(1)
C.3.2 Warm-up: Music Synthesis	433	(5)
C.3.2.1 D-to-A Conversion	434	(1)
C.3.2.2 Theory of Sampling	434	(1)
C.3.2.3 Piano Keyboard	435	(3)
C.3.3 Lab: Synthesis of Musical Notes	438	(4)
C.3.3.1 Spectrogram of the Music	439	(1)
C.3.3.2 Fur Elise	439	(1)
C.3.3.3 Musical Tweaks	440	(1)
C.3.3.4 Programming Tips	440	(1)
C.3.3.5 Alternative Piece: Jesu, Joy of Man's Desiring	441	(1)
C.3.3.6 Alternative Piece: Minuet in G	441	(1)
C.3.3.7 Alternative Piece: Beethoven's Fifth Symphony	441	(1)
C.3.3.8 Alternative Piece: Twinkle, Twinkle, Little Star	442	(1)
C.3.4 Sound Evaluation Criteria	442	(1)
C.4 Laboratory: AM and FM Sinusoidal Signals	443	(13)
C.4.1 Overview	443	(2)
C.4.1.1 Amplitude Modulation	443	(1)
C.4.1.2 Frequency Modulated Signals	443	(1)
C.4.1.3 Chirp, or Linearly Swept Frequency	444	(1)
C.4.1.4 Advanced Topic: Spectrograms	444	(1)
C.4.2 Warm-up	445	(1)
C.4.2.1 MATLAB Synthesis of Chirp Signals	445	(1)
C.4.3 Lab A: Chirps and Beats	446	(2)
C.4.3.1 Synthesize a Chirp	446	(1)
C.4.3.2 Beat Notes	446	(1)
C.4.3.3 More on Spectrograms (Optional)	447	(1)
C.4.4 Lab B: FM Synthesis of Instrument Sounds	448	(4)
C.4.4.1 Generating the Bell Envelopes	449	(1)
C.4.4.2 Parameters for the Bell	450	(1)
C.4.4.3 The Bell Sound	451	(1)
C.4.4.4 Comments about the Bell	452	(1)
C.4.5 Woodwinds	452	(4)
C.4.5.1 Generating the Envelopes for Woodwinds	452	(1)
C.4.5.2 Scaling the Clarinet Envelopes	453	(1)
C.4.5.3 Clarinet Envelopes	453	(1)
C.4.5.4 Parameters for the Clarinet	454	(1)
C.4.5.5 Experiment with the Clarinet Sound	455	(1)
C.5 Laboratory: FIR Filtering of Sinusoidal Waveforms	456	(7)
C.5.1 Overview of Filtering	456	(2)
C.5.1.1 Frequency Response of FIR Filters	457	(1)
C.5.2 Warm-up	458	(1)
C.5.2.1 Frequency Response of the 3-Point Averager	458	(1)
C.5.3 Lab: FIR Filters	459	(4)
C.5.3.1 Filtering Cosine Waves	459	(1)
C.5.3.2 First-Difference Filter	460	(1)
C.5.3.3 Linearity of the Filter	460	(1)
C.5.3.4 Time Invariance of the Filter	461	(1)
C.5.3.5 Cascading Two Systems	461	(2)
C.6 Laboratory: Filtering Sampled Waveforms	463	(6)
C.6.1 Overview of Linear Filters	463	(1)
C.6.2 Warm-up	464	(1)
C.6.2.1 Properties of Discrete-Time Filters	464	(1)
C.6.3 Laboratory: Sampling and Filters	465	(4)
C.6.3.1 Filtering a Stair-Step Signal	465	(1)
C.6.3.2 Implementation of Five-Point Averager	466	(1)
C.6.3.3 Implementation of First-Difference System	466	(1)
C.6.3.4 Implementation of First Cascade (Fig. C.11)	467	(1)
C.6.3.5 Implementation of Second Cascade (Fig. C.12)	467	(1)
C.6.3.6 Comparison of Systems of Figs. C.11 and C.12	467	(1)
C.6.3.7 Filtering the Speech Waveform	467	(2)
C.7 Laboratory: Everyday Sinusoidal Signals	469	(12)
C.7.1 Background	469	(5)
C.7.1.1 Background A: Telephone Touch Tone Dialing	469	(1)
C.7.1.2 DTMF Decoding	470	(1)
C.7.1.3 Background B: Amplitude Modulation (AM)	470	(2)
C.7.1.4 AM Demodulation	472	(1)
C.7.1.5 Envelope Detection (Peak Tracking)	472	(1)
C.7.1.6 LTI filter-based demodulation	473	(1)
C.7.1.7 Notch Filters for Demodulation	473	(1)
C.7.2 Warm-up A: DTMF Synthesis	474	(1)
C.7.2.1 DTMF Dial Function	474	(1)
C.7.3 Warm-up B: Tone Amplitude Modulation	475	(1)
C.7.4 Laboratory A: DTMF Decoding	475	(3)
C.7.4.1 Filter Design	475	(1)
C.7.4.2 A Scoring Function	476	(1)
C.7.4.3 DTMF Decode Function	477	(1)
C.7.4.4 Telephone Numbers	478	(1)
C.7.5 Laboratory B: AM Waveform Detection	478	(1)
C.7.6 Optional: Amplitude Modulation with Speech	479	(2)
C.8 Laboratory: Filtering and Edge Detection of Images	481	(11)
C.8.1 Overview	481	(2)
C.8.1.1 Digital Images	481	(1)
C.8.1.2 Displaying Images	481	(2)
C.8.1.3 Image Filtering	483	(1)
C.8.2 Warm-up: Display of Images	483	(1)
C.8.2.1 Display Test	484	(1)
C.8.3 Laboratory: Filtering Images	484	(8)
C.8.3.1 One-Dimensional Filtering	484	(1)
C.8.3.2 Blurring an Image	485	(1)
C.8.3.3 More Image Filters	486	(1)
C.8.3.4 Frequency Content of an Image	486	(2)
C.8.3.5 The Method of Synthetic Highs	488	(1)
C.8.3.6 Nonlinear Filters	489	(1)
C.8.3.7 Edges in an Image	489	(1)
C.8.3.8 The Slope-Threshold Function	490	(1)
C.8.3.9 What's Nonlinear about Edge Detection?	491	(1)
C.9 Laboratory: Sampling and Zooming of Images	492	(5)
C.9.1 Overview	492	(1)
C.9.2 Warm-up: Linear Interpolation	492	(1)
C.9.3 Laboratory: Sampling of Images	493	(4)
C.9.3.1 Reconstruction of Images	494	(1)
C.9.3.2 Zooming for an Image	495	(2)
C.10 Laboratory: The z-, n-, and w-Domains	497	(5)
C.10.1 Objective	497	(1)
C.10.2 Warm-up	497	(1)
C.10.3 Laboratory: Relationships Between z-, n-, and w-domains	497	(1)
C.10.4 Real Poles	498	(1)
C.10.5 Complex Poles	498	(1)
C.10.6 Filter Design	499	(3)
C.11 Laboratory: Extracting Frequencies of Musical Tones	502	(6)
C.11.1 Overview	502	(1)
C.11.2 Warm-up: System Components	502	(3)
C.11.2.1 Spectrogram Computation	502	(2)
C.11.2.2 Generating the Window	504	(1)
C.11.2.3 Display the Spectrogram	504	(1)
C.11.2.4 Finding Peaks	504	(1)
C.11.3 Design of the Music-Writing System	505	(2)
C.11.3.1 Block Diagram for the System	505	(1)
C.11.3.2 Write a Spectrogram Function	505	(1)
C.11.3.3 Parameters of the Spectrogram	506	(1)
C.11.3.4 Peak Picking and Editing	506	(1)
C.11.3.5 Writing the Musical Score	507	(1)
C.11.4 Testing the Music Extraction Program	507	(1)
Appendix D About the CD	508	(11)
Index	519