DSP First, 2nd edition
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Overview
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.
Published by Pearson (January 1st 2022)  Copyright © 2016
ISBN13: 9780137848188
Subject: Electrical Engineering
Category: Digital Signals & Systems
Overview
Introduction
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
23Sinusoidal Signals
23.1Relation of Frequency to Period
23.2 Phase and Time Shift
24 Sampling and Plotting Sinusoids
25Complex 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
26Phasor 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
28Time 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
Problems Frequency 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
Your questions answered
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