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This title in other editionsDSP Firstby James H. Mcclellan
Synopses & ReviewsPublisher Comments:For introductory courses (freshman and sophomore courses) in Digital Signal Processing and Signals and Systems. Text may be used before the student has taken a course in circuits.
DSP First and it's accompanying digital assets are the result of more than 20 years of work that originated from, and was guided by, the premise that signal processing is the best starting point for the study of electrical and computer engineering. The "DSP First" approach introduces the use of mathematics as the language for thinking about engineering problems, lays the groundwork for subsequent courses, and gives students handson experiences with MATLAB.
The Second Edition features three new chapters on the Fourier Series, DiscreteTime Fourier Transform, and the The Discrete Fourier Transform as well as updated labs, visual demos, an update to the existing chapters, and hundreds of new homework problems and solutions.
Synopsis:Designed and written by experienced and wellrespected authors, this hands on, multimedia package provides a motivating introduction to fundamental concepts, specifically discretetime systems. Unique features such as visual learning demonstrations, MATLAB laboratories and a bank of solved problems are just a few things that make this an essential learning tool for mastering fundamental concepts in today's electrical and computer engineering forum. Covers basic DSP concepts, integrated laboratory projectsrelated to music, sound and image processing. Other topics include new MATLAB functions for basic DSP operations, Sinusoids, Spectrum Representation, Sampling and Aliasing, FIR Filters, Frequency Response of FIR Filters, zTransforms, IIR Filters, and Spectrum Analysis. Useful as a selfteaching tool for anyone eager to discover more about DSP applications, multimedia signals, and MATLAB.
About the AuthorDr. James H. McClellan received the B.S. degree in Electrical Engineering from Louisiana State University in 1969 and the M.S. and Ph.D. degrees from Rice University in 1972 and 1973, respectively. During 19734 he was a member of the research staff at M.I.T.'s Lincoln Laboratory. He then became a professor in the Electrical Engineering and Computer Science Department at M.I.T. In 1982, he joined Schlumberger Well Services where he worked on the application of 2D spectral estimation to the processing of dispersive sonic waves, and the implementation of signal processing algorithms for dedicated highspeed array processors. He has been at Georgia Tech since 1987. Prof. McClellan is a Fellow of the IEEE and he received the ASSP Technical Achievement Award in 1987, and then the Signal Processing Society Award in 1996.
Ronald W. Schafer is an electrical engineer notable for his contributions to digital signal processing. After receiving his Ph.D. degree at MIT in 1968, he joined the Acoustics Research Department at Bell Laboratories, where he did research on digital signal processing and digital speech coding. He came to the Georgia Institute of Technology in 1974, where he stayed until joining Hewlett Packard in March 2005. He has served as Associate Editor of IEEE Transactions on Acoustics, Speech, and Signal Processing and as VicePresident and President of the IEEE Signal Processing Society. He is a Life Fellow of the IEEE and a Fellow of the Acoustical Society of America. He has received the IEEE Region 3 Outstanding Engineer Award, the 1980 IEEE Emanuel R. Piore Award, the Distinguished Professor Award at the Georgia Institute of Technology, the 1992 IEEE Education Medal and the 2010 IEEE Jack S. Kilby Signal Processing Medal.
Table of ContentsIntroduction 11 Mathematical Representation of Signals 12 Mathematical Representation of Systems 13 Systems as Building Blocks 14 The Next Step
Sinusoids 21 Tuning Fork Experiment 22 Review of Sine and Cosine Functions 23 Sinusoidal Signals 23.1 Relation of Frequency to Period 23.2 Phase and Time Shift 24 Sampling and Plotting Sinusoids 25 Complex Exponentials and Phasors 25.1 Review of Complex Numbers 25.2 Complex Exponential Signals 25.3 The Rotating Phasor Interpretation 25.4 Inverse Euler Formulas Phasor Addition 26 Phasor Addition 26.1 Addition of Complex Numbers 26.2 Phasor Addition Rule 26.3 Phasor Addition Rule: Example 26.4 MATLAB Demo of Phasors 26.5 Summary of the Phasor Addition Rule Physics of the Tuning Fork 27.1 Equations from Laws of Physics 27.2 General Solution to the Differential Equation 27.3 Listening to Tones 28 Time Signals: More Than Formulas Summary and Links Problems
Spectrum Representation 31 The Spectrum of a Sum of Sinusoids 31.1 Notation Change 31.2 Graphical Plot of the Spectrum 31.3 Analysis vs. Synthesis Sinusoidal Amplitude Modulation 32.1 Multiplication of Sinusoids 32.2 Beat Note Waveform 32.3 Amplitude Modulation 32.4 AM Spectrum 32.5 The Concept of Bandwidth Operations on the Spectrum 33.1 Scaling or Adding a Constant 33.2 Adding Signals 33.3 TimeShifting x.t/ Multiplies ak by a Complex Exponential 33.4 Differentiating x.t/ Multiplies ak by .j 2nfk/ 33.5 Frequency Shifting Periodic Waveforms 34.1 Synthetic Vowel 34.3 Example of a Nonperiodic Signal Fourier Series 35.1 Fourier Series: Analysis 35.2 Analysis of a FullWave Rectified Sine Wave 35.3 Spectrum of the FWRS Fourier Series 35.3.1 DC Value of Fourier Series 35.3.2 Finite Synthesis of a FullWave Rectified Sine Time–Frequency Spectrum 36.1 Stepped Frequency 36.2 Spectrogram Analysis Frequency Modulation: Chirp Signals 37.1 Chirp or Linearly Swept Frequency 37.2 A Closer Look at Instantaneous Frequency Summary and Links Problems
Fourier Series Fourier Series Derivation
41.1 Fourier Integral Derivation Examples of Fourier Analysis 42.1 The Pulse Wave 42.1.1 Spectrum of a Pulse Wave 42.1.2 Finite Synthesis of a Pulse Wave 42.2 Triangle Wave 42.2.1 Spectrum of a Triangle Wave 42.2.2 Finite Synthesis of a Triangle Wave 42.3 HalfWave Rectified Sine 42.3.1 Finite Synthesis of a HalfWave Rectified Sine Operations on Fourier Series 43.1 Scaling or Adding a Constant 43.2 Adding Signals 43.3 TimeScaling 43.4 TimeShifting x.t/ Multiplies ak by a Complex Exponential 43.5 Differentiating x.t/ Multiplies ak by .j!0k/ 43.6 Multiply x.t/ by Sinusoid Average Power, Convergence, and Optimality 44.1 Derivation of Parseval’s Theorem 44.2 Convergence of Fourier Synthesis 44.3 Minimum MeanSquare Approximation PulsedDoppler Radar Waveform 45.1 Measuring Range and Velocity Problems
Sampling and Aliasing Sampling
51.1 Sampling Sinusoidal Signals 51.2 The Concept of Aliasing 51.3 Spectrum of a DiscreteTime Signal 51.4 The Sampling Theorem 51.5 Ideal Reconstruction Spectrum View of Sampling and Reconstruction 52.1 Spectrum of a DiscreteTime Signal Obtained by Sampling 52.2 OverSampling 52.3 Aliasing Due to UnderSampling 52.4 Folding Due to UnderSampling 52.5 Maximum Reconstructed Frequency Strobe Demonstration 53.1 Spectrum Interpretation DiscretetoContinuous Conversion 54.1 Interpolation with Pulses 54.2 ZeroOrder Hold Interpolation 54.3 Linear Interpolation 54.4 Cubic Spline Interpolation 54.5 OverSampling Aids Interpolation 54.6 Ideal Bandlimited Interpolation The Sampling Theorem Summary and Links Problems
FIR Filters 61 DiscreteTime Systems 62 The RunningAverage Filter 63 The General FIR Filter 63.1 An Illustration of FIR Filtering The Unit Impulse Response and Convolution 64.1 Unit Impulse Sequence 64.2 Unit Impulse Response Sequence 64.2.1 The UnitDelay System 64.3 FIR Filters and Convolution 64.3.1 Computing the Output of a Convolution 64.3.2 The Length of a Convolution 64.3.3 Convolution in MATLAB 64.3.4 Polynomial Multiplication in MATLAB 64.3.5 Filtering the UnitStep Signal 64.3.6 Convolution is Commutative 64.3.7 MATLAB GUI for Convolution Implementation of FIR Filters 65.1 Building Blocks 65.1.1 Multiplier 65.1.2 Adder 65.1.3 Unit Delay 65.2 Block Diagrams 65.2.1 Other Block Diagrams 65.2.2 Internal Hardware Details Linear TimeInvariant (LTI) Systems 66.1 Time Invariance 66.2 Linearity 66.3 The FIR Case Convolution and LTI Systems 67.1 Derivation of the Convolution Sum 67.2 Some Properties of LTI Systems Cascaded LTI Systems Example of FIR Filtering Summary and Links
ProblemsFrequency Response of FIR Filters 71 Sinusoidal Response of FIR Systems 72 Superposition and the Frequency Response 73 SteadyState and Transient Response 74 Properties of the Frequency Response 74.1 Relation to Impulse Response and Difference Equation 74.2 Periodicity of H.ej !O / 74.3 Conjugate Symmetry Graphical Representation of the Frequency Response 75.1 Delay System 75.2 FirstDifference System 75.3 A Simple Lowpass Filter Cascaded LTI Systems RunningSum Filtering 77.1 Plotting the Frequency Response 77.2 Cascade of Magnitude and Phase 77.3 Frequency Response of Running Averager 77.4 Experiment: Smoothing an Image Filtering Sampled ContinuousTime Signals 78.1 Example: Lowpass Averager 78.2 Interpretation of Delay Summary and Links Problems
The DiscreteTime Fourier Transform DTFT: DiscreteTime Fourier Transform
81.1 The DiscreteTime Fourier Transform 81.1.1 DTFT of a Shifted Impulse Sequence 81.1.2 Linearity of the DTFT 81.1.3 Uniqueness of the DTFT 81.1.4 DTFT of a Pulse 81.1.5 DTFT of a RightSided Exponential Sequence 81.1.6 Existence of the DTFT 81.2 The Inverse DTFT 81.2.1 Bandlimited DTFT 81.2.2 Inverse DTFT for the RightSided Exponential 81.3 The DTFT is the Spectrum Properties of the DTFT 82.1 The Linearity Property 82.2 The TimeDelay Property 82.3 The FrequencyShift Property 82.3.1 DTFT of a Complex Exponential 82.3.2 DTFT of a Real Cosine Signal 82.4 Convolution and the DTFT 82.4.1 Filtering is Convolution 82.5 Energy Spectrum and the Autocorrelation Function 82.5.1 Autocorrelation Function Ideal Filters 83.1 Ideal Lowpass Filter 83.2 Ideal Highpass Filter 83.3 Ideal Bandpass Filter Practical FIR Filters 84.1 Windowing 84.2 Filter Design 84.2.1 Window the Ideal Impulse Response 84.2.2 Frequency Response of Practical Filters 84.2.3 Passband Defined for the Frequency Response 84.2.4 Stopband Defined for the Frequency Response 84.2.5 Transition Zone of the LPF 84.2.6 Summary of Filter Specifications 84.3 GUI for Filter Design Table of Fourier Transform Properties and Pairs Summary and Links Problems
The Discrete Fourier Transform Discrete Fourier Transform (DFT)
91.1 The Inverse DFT 91.2 DFT Pairs from the DTFT 91.2.1 DFT of Shifted Impulse 91.2.2 DFT of Complex Exponential 91.3 Computing the DFT 91.4 Matrix Form of the DFT and IDFT Properties of the DFT 92.1 DFT Periodicity for XŒk] 92.2 Negative Frequencies and the DFT 92.3 Conjugate Symmetry of the DFT 92.3.1 Ambiguity at XŒN=2] 92.4 Frequency Domain Sampling and Interpolation 92.5 DFT of a Real Cosine Signal Inherent Periodicity of xŒn] in the DFT 93.1 DFT Periodicity for xŒn] 93.2 The Time Delay Property for the DFT 93.2.1 Zero Padding 93.3 The Convolution Property for the DFT Table of Discrete Fourier Transform Properties and Pairs Spectrum Analysis of Discrete Periodic Signals 95.1 Periodic Discretetime Signal: Fourier Series 95.2 Sampling Bandlimited Periodic Signals 95.3 Spectrum Analysis of Periodic Signals Windows 96.0.1 DTFT of Windows The Spectrogram 97.1 An Illustrative Example 97.2 TimeDependent DFT 97.3 The Spectrogram Display 97.4 Interpretation of the Spectrogram 97.4.1 Frequency Resolution 97.5 Spectrograms in MATLAB The Fast Fourier Transform (FFT) 98.1 Derivation of the FFT 98.1.1 FFT Operation Count Summary and Links Problems zTransforms Definition of the zTransform Basic zTransform Properties 102.1 Linearity Property of the zTransform 102.2 TimeDelay Property of the zTransform 102.3 A General zTransform Formula The zTransform and Linear Systems 103.1 UnitDelay System 103.2 z1 Notation in Block Diagrams 103.3 The zTransform of an FIR Filter 103.4 zTransform of the Impulse Response 103.5 Roots of a ztransform Polynomial Convolution and the zTransform 104.1 Cascading Systems 104.2 Factoring zPolynomials 104.3 Deconvolution Relationship Between the zDomain and the !O Domain 105.1 The zPlane and the Unit Circle The Zeros and Poles of H.z/ 106.1 PoleZero Plot 106.2 Significance of the Zeros of H.z/ 106.3 Nulling Filters 106.4 Graphical Relation Between z and !O 106.5 ThreeDomain Movies Simple Filters 107.1 Generalize the LPoint RunningSum Filter 107.2 A Complex Bandpass Filter 107.3 A Bandpass Filter with Real Coefficients
Practical Bandpass Filter Design Properties of LinearPhase Filters
109.1 The LinearPhase Condition 109.2 Locations of the Zeros of FIR LinearPhase Systems Summary and Links Problems IIR Filters
The General IIR Difference Equation TimeDomain Response
112.1 Linearity and Time Invariance of IIR Filters 112.2 Impulse Response of a FirstOrder IIR System 112.3 Response to FiniteLength Inputs 112.4 Step Response of a FirstOrder Recursive System System Function of an IIR Filter 113.1 The General FirstOrder Case 113.2 H.z/ from the Impulse Response 113.3 The zTransform Method The System Function and BlockDiagram Structures 114.1 Direct Form I Structure 114.2 Direct Form II Structure 114.3 The Transposed Form Structure Poles and Zeros 115.1 Roots in MATLAB 115.2 Poles or Zeros at z D 0 or 1 115.3 Output Response from Pole Location Stability of IIR Systems 116.1 The Region of Convergence and Stability Frequency Response of an IIR Filter 117.1 Frequency Response using MATLAB 117.2 ThreeDimensional Plot of a System Function Three Domains The Inverse zTransform and Some Applications 119.1 Revisiting the Step Response of a FirstOrder System 119.2 A General Procedure for Inverse zTransformation
SteadyState Response and Stability SecondOrder Filters
1111.1 zTransform of SecondOrder Filters 1111.2 Structures for SecondOrder IIR Systems 1111.3 Poles and Zeros 1111.4 Impulse Response of a SecondOrder IIR System 1111.4.1 Distinct Real Poles 1111.5 Complex Poles Frequency Response of SecondOrder IIR Filter 1112.1 Frequency Response via MATLAB 1112.23dB Bandwidth 1112.3 ThreeDimensional Plot of System Functions Example of an IIR Lowpass Filter Summary and Links Problems What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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