| |
| |
| |
Useful Information (inside cover / endpaper) | |
| |
| |
| |
Identities | |
| |
| |
| |
Definite Integrals | |
| |
| |
| |
Infinite Series | |
| |
| |
| |
Orthogonality | |
| |
| |
| |
Signal Inner Product | |
| |
| |
| |
Convolution | |
| |
| |
| |
Fourier Series | |
| |
| |
| |
Complex Fourier Series | |
| |
| |
| |
Fourier Transform | |
| |
| |
| |
Laplace Transform | |
| |
| |
| |
z-Transform | |
| |
| |
| |
List of Acronyms | |
| |
| |
| |
Introduction to Signals and Systems | |
| |
| |
| |
Introduction | |
| |
| |
| |
What is a Signal? | |
| |
| |
| |
What is a System? | |
| |
| |
| |
Introduction to Signal Manipulation | |
| |
| |
| |
Linear Combination | |
| |
| |
| |
Addition and Multiplication of Signals | |
| |
| |
| |
Visualizing Signals - An Important Skill | |
| |
| |
| |
Introduction to Signal Manipulation Using MATLAB | |
| |
| |
Defining Signals | |
| |
| |
Basic Plotting Commands | |
| |
| |
Multiple Plots on One Figure | |
| |
| |
| |
A Few Useful Signals | |
| |
| |
| |
The Unit Rectangle rect(t) | |
| |
| |
| |
The Unit Step u(t) | |
| |
| |
| |
Reection about t = 0 | |
| |
| |
| |
The Exponential ext | |
| |
| |
| |
The Unit Impulse _(t) | |
| |
| |
The Sifting Property of _(t) | |
| |
| |
Sampling Function | |
| |
| |
| |
The Sinusoidal Signal | |
| |
| |
| |
The One-Sided Cosine Graph | |
| |
| |
| |
Phase Change - _ | |
| |
| |
| |
Sine vs Cosine | |
| |
| |
Combining Signals: The Gated Sine Wave | |
| |
| |
Combining Signals: A Dial Tone Generator | |
| |
| |
| |
Useful Hints and Help with MATLAB | |
| |
| |
| |
Annotating Graphs | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
Classification of Signals | |
| |
| |
| |
Introduction | |
| |
| |
| |
Periodic Signals | |
| |
| |
| |
Sinusoid | |
| |
| |
| |
Half-wave Rectified Sinusoid | |
| |
| |
| |
Full-wave Rectified Sinusoid | |
| |
| |
| |
Square Wave | |
| |
| |
| |
Sawtooth Wave | |
| |
| |
| |
Pulse Train | |
| |
| |
| |
Rectangular Wave | |
| |
| |
| |
Triangle wave | |
| |
| |
| |
Impulse Train | |
| |
| |
| |
Odd and Even Signals | |
| |
| |
| |
Combining Odd and Even signals | |
| |
| |
| |
The constant value s(t) = A | |
| |
| |
| |
Trigonometric Identities | |
| |
| |
| |
The Modulation Property | |
| |
| |
| |
Energy and Power Signals | |
| |
| |
| |
Periodic Signals = Power Signals | |
| |
| |
| |
Comparing Signal Power: The Decibel (dB) | |
| |
| |
| |
Complex Signals | |
| |
| |
| |
Discrete Time Signals | |
| |
| |
| |
Digital Signals | |
| |
| |
| |
} Random Signals | |
| |
| |
| |
Useful Hints and Help with MATLAB | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
Linear Systems | |
| |
| |
| |
Introduction | |
| |
| |
| |
Definition of a Linear System | |
| |
| |
| |
Superposition | |
| |
| |
| |
Linear System Exercise 1: Zero State Response | |
| |
| |
Zero Input ! Zero Output | |
| |
| |
| |
Linear System Exercise 2: Operating in a linear region | |
| |
| |
Non-Linear Components | |
| |
| |
| |
Linear System Exercise 3: Mixer | |
| |
| |
A System is defined by its Response Function | |
| |
| |
| |
Linear Time-Invariant (LTI) Systems | |
| |
| |
| |
Bounded Input, Bounded Output | |
| |
| |
| |
System Behavior as a Black Box | |
| |
| |
| |
Linear System Response Function h(t) | |
| |
| |
| |
Convolution | |
| |
| |
| |
The Convolution Integral | |
| |
| |
| |
Convolution is Commutative | |
| |
| |
| |
Convolution is Associative | |
| |
| |
| |
Convolution is Distributive over Addition | |
| |
| |
| |
Evaluation of the Convolution Integral | |
| |
| |
| |
Convolution Properties | |
| |
| |
A Pulse Input Signal | |
| |
| |
| |
Convolution with MATLAB | |
| |
| |
| |
Determining h(t) in an Unknown System | |
| |
| |
| |
The Unit Impulse _(t) Test Signal | |
| |
| |
| |
Convolution and Signal Decomposition | |
| |
| |
| |
An Ideal Distortionless System | |
| |
| |
| |
Causality | |
| |
| |
| |
Causality and Zero Input Response | |
| |
| |
| |
Combined Systems | |
| |
| |
| |
} Convolution and Random Numbers | |
| |
| |
| |
Useful Hints and Help with MATLAB | |
| |
| |
| |
Chapter Summary | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
The Fourier Series | |
| |
| |
| |
Introduction | |
| |
| |
| |
Expressing Signals by Components | |
| |
| |
| |
Approximating a Signal s(t) by Another: The Signal Inner Product | |
| |
| |
| |
Estimating One Signal by Another | |
| |
| |
| |
Part One - Orthogonal Signals | |
| |
| |
| |
Orthogonality | |
| |
| |
| |
An Orthogonal Signal Space | |
| |
| |
| |
The Signal Inner Product Formulation | |
| |
| |
| |
Complete Set of Orthogonal Signals | |
| |
| |
| |
What if a Complete Set is not Present? | |
| |
| |
| |
An Orthogonal Set of Signals | |
| |
| |
| |
Orthogonal Signals and Linearly Independent Equations | |
| |
| |
| |
Part Two - The Fourier Series | |
| |
| |
| |
A Special set of Orthogonal Functions | |
| |
| |
| |
The Fourier Series - An Orthogonal Set? | |
| |
| |
| |
Computing Fourier Series Components | |
| |
| |
| |
Fourier Series Approximation to an Odd Square Wave | |
| |
| |
| |
Zero-Frequency (DC) Component | |
| |
| |
| |
Fundamental Frequency Component | |
| |
| |
| |
Higher Order Components | |
| |
| |
| |
Frequency Spectrum of the Square Wave s(t) | |
| |
| |
| |
Practical Harmonics | |
| |
| |
| |
The 60 Hz Power Line | |
| |
| |
| |
Audio Amplifier Specs - Total Harmonic Distortion | |
| |
| |
| |
The CB Radio Booster | |
| |
| |
| |
Odd and Even Square Waves | |
| |
| |
| |
The Fourier Series Components of an Even Square Wave | |
| |
| |
| |
Gibb's Phenomenon | |
| |
| |
| |
Setting-Up the Fourier Series Calculation | |
| |
| |
| |
Appearance of Pulse Train Frequency Components | |
| |
| |
| |
Some Common Fourier Series | |
| |
| |
| |
Part Three: The Complex Fourier Series | |
| |
| |
| |
Not all Signals are Even or Odd | |
| |
| |
| |
The Complex Fourier Series | |
| |
| |
| |
Complex Fourier Series - The Frequency Domain | |
| |
| |
| |
Comparing the Real and Complex Fourier Series | |
| |
| |
| |
Magnitude and Phase | |
| |
| |
| |
Complex Fourier Series Components | |
| |
| |
| |
Real Signals and the Complex Fourier Series | |
| |
| |
| |
Stretching and Squeezing: Time vs Frequency | |
| |
| |
| |
Shift in Time | |
| |
| |
| |
Change in Amplitude | |
| |
| |
| |
Power in Periodic Signals | |
| |
| |
| |
Parseval's Theorem for Periodic Signals | |
| |
| |
| |
Properties of the Complex Fourier Series | |
| |
| |
| |
Analysis of a DC Power Supply | |
| |
| |
| |
The DC Component | |
| |
| |
| |
An AC-DC Converter | |
| |
| |
| |
Vrms is always greater than or equal to Vdc | |
| |
| |
| |
Fourier Series: The Full-wave Rectifier | |
| |
| |
| |
Complex Fourier series components Cn | |
| |
| |
| |
The Fourier Series with MATLAB | |
| |
| |
| |
Essential features of the fft() in MATLAB | |
| |
| |
| |
Full-wave Rectified Cosine (60 Hz) | |
| |
| |
| |
Useful Hints and Help with MATLAB | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
Orthogonal Signals | |
| |
| |
| |
The Fourier Series | |
| |
| |
| |
The Fourier Transform | |
| |
| |
| |
Introduction | |
| |
| |
| |
A Fresh Look at the Fourier Series | |
| |
| |
| |
Approximating a Non-Periodic Signal Over All Time | |
| |
| |
| |
Definition of the Fourier Transform | |
| |
| |
| |
Existence of the Fourier Transform | |
| |
| |
| |
The Inverse Fourier Transform | |
| |
| |
| |
Properties of the Fourier Transform | |
| |
| |
| |
Linearity of the Fourier Transform | |
| |
| |
| |
Value of the Fourier transform at the Origin | |
| |
| |
| |
Odd and Even Functions and the Fourier Transform | |
| |
| |
| |
The Rectangle Signal | |
| |
| |
| |
The Sinc Function | |
| |
| |
| |
Expressing a Function in Terms of sinc(t) | |
| |
| |
| |
The Fourier Transform of a General Rectangle | |
| |
| |
| |
Magnitude of the Fourier Transform | |
| |
| |
| |
Signal Manipulations: Time and Frequency | |
| |
| |
| |
Amplitude Variations | |
| |
| |
| |
Stretch and Squeeze: The Sinc Function | |
| |
| |
| |
The Scaling Theorem | |
| |
| |
| |
Testing the Limits | |
| |
| |
| |
A Shift in Time | |
| |
| |
| |
The Shifting Theorem | |
| |
| |
| |
The Fourier Transform of a Shifted Rectangle | |
| |
| |
| |
Impulse Series - The Line Spectrum | |
| |
| |
| |
Shifted Impulse _(f f0) | |
| |
| |
| |
Fourier Transform of a Periodic Signal | |
| |
| |
| |
Fourier Transform Pairs | |
| |
| |
| |
The Illustrated Fourier Transform | |
| |
| |
| |
Rapid Changes vs High Frequencies | |
| |
| |
| |
Derivative Theorem | |
| |
| |
| |
Integration Theorem | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
Practical Fourier Transforms | |
| |
| |
| |
Introduction | |
| |
| |
| |
Convolution: Time and Frequency | |
| |
| |
| |
Simplifying the Convolution Integral | |
| |
| |
| |
Transfer Function of a Linear System | |
| |
| |
| |
Impulse Response: The Frequency Domain | |
| |
| |
| |
Frequency Response Curve | |
| |
| |
| |
Energy in Signals: Parseval's Theorem for the Fourier Transform | |
| |
| |
| |
Energy Spectral Density | |
| |
| |
| |
Data Smoothing and the Frequency Domain | |
| |
| |
| |
Ideal Filters | |
| |
| |
| |
The Ideal Lowpass Filter is not Causal | |
| |
| |
| |
A Real Lowpass Filter | |
| |
| |
| |
The Modulation Theorem | |
| |
| |
| |
A Voice Privacy System | |
| |
| |
| |
Periodic Signals and the Fourier Transform | |
| |
| |
| |
The Impulse Train | |
| |
| |
| |
General Appearance of Periodic Signals | |
| |
| |
| |
The Fourier Transform of a Square wave | |
| |
| |
| |
Other Periodic Waveforms | |
| |
| |
| |
The Analog Spectrum Analyzer | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
The Laplace Transform | |
| |
| |
| |
Introduction | |
| |
| |
| |
The Laplace Transform | |
| |
| |
| |
The Frequency Term ej!t | |
| |
| |
| |
The Exponential Term e_t | |
| |
| |
| |
The s-domain | |
| |
| |
| |
Exploring the s-domain | |
| |
| |
| |
A Pole at the origin | |
| |
| |
Graphing the function H(s) = 1=s | |
| |
| |
| |
Decaying Exponential | |
| |
| |
| |
A Sinusoid | |
| |
| |
The Generalized Cosine: A = cos(!t + _) | |
| |
| |
| |
A Decaying Sinusoid | |
| |
| |
| |
An Unstable System | |
| |
| |
| |
Visualizing the Laplace Transform | |
| |
| |
| |
First Order Lowpass Filter | |
| |
| |
| |
Pole Position Determines Frequency Response | |
| |
| |
| |
Second Order Lowpass Filter | |
| |
| |
Resonance Frequency | |
| |
| |
Multiple Poles and Zeros | |
| |
| |
| |
Two-Sided Laplace Transform | |
| |
| |
| |
The Bode Plot | |
| |
| |
Bode Plot - Multiple Poles and Zeros | |
| |
| |
| |
System Analysis in MATLAB | |
| |
| |
| |
Properties of the Laplace Transform | |
| |
| |
| |
Differential Equations | |
| |
| |
| |
Solving a Differential Equation | |
| |
| |
Compound Interest | |
| |
| |
| |
Transfer Function as Differential Equations | |
| |
| |
| |
Laplace Transform Pairs | |
| |
| |
| |
The Illustrated Laplace Transform | |
| |
| |
| |
Circuit Analysis with the Laplace Transform | |
| |
| |
| |
Voltage Divider | |
| |
| |
| |
A First-Order Lowpass Filter | |
| |
| |
| |
A First-Order Highpass Filter | |
| |
| |
| |
A Second Order Filter | |
| |
| |
Lowpass Filter | |
| |
| |
Bandpass Filter | |
| |
| |
Highpass Filter | |
| |
| |
Analysis of a Second Order System | |
| |
| |
Series RLC Circuit Analysis | |
| |
| |
| |
State Variable Analysis | |
| |
| |
| |
State Variable Analysis - First Order System | |
| |
| |
| |
First Order State Space Analysis with MATLAB | |
| |
| |
| |
State Variable Analysis - Second Order System | |
| |
| |
| |
Matrix Form of the State Space Equations | |
| |
| |
| |
Second Order State Space Analysis with MATLAB | |
| |
| |
| |
Differential Equation | |
| |
| |
| |
State Space and Transfer Functions with MATLAB | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
Discrete Signals | |
| |
| |
| |
Introduction | |
| |
| |
| |
Discrete Time vs Continuous Time Signals | |
| |
| |
| |
1 Digital Signal Processing | |
| |
| |
| |
A Discrete Time Signal | |
| |
| |
| |
1 A Periodic Discrete Time Signal | |
| |
| |
| |
Data Collection and Sampling Rate | |
| |
| |
| |
The Selection of a Sampling Rate | |
| |
| |
| |
Bandlimited Signal | |
| |
| |
| |
Theory of Sampling | |
| |
| |
| |
The Sampling Function | |
| |
| |
| |
Recovering a Waveform from Samples | |
| |
| |
| |
A Practical Sampling Signal | |
| |
| |
| |
Minimum Sampling Rate | |
| |
| |
| |
Nyquist Sampling Rate | |
| |
| |
| |
The Nyquist Sampling Rate is a Theoretical Minimum | |
| |
| |
| |
Sampling Rate and Alias Frequency | |
| |
| |
| |
Practical Aliasing | |
| |
| |
| |
Analysis of Aliasing | |
| |
| |
| |
Anti-Alias Filter | |
| |
| |
| |
Introduction to Digital Filtering | |
| |
| |
| |
Impulse Response Function | |
| |
| |
| |
A Simple Discrete Response Function | |
| |
| |
| |
Delay Blocks are a Natural Consequence of Sampling | |
| |
| |
| |
General Digital Filtering | |
| |
| |
| |
The Fourier Transform of Sampled Signals | |
| |
| |
| |
The Discrete Fourier Transform (DFT) | |
| |
| |
| |
A Discrete Fourier Series | |
| |
| |
| |
Computing the Discrete Fourier Transform (DFT) | |
| |
| |
| |
The Fast Fourier Transform (FFT) | |
| |
| |
| |
Illustrative Examples | |
| |
| |
| |
FFT and Sample Rate | |
| |
| |
| |
Practical DFT Issues | |
| |
| |
Constructing the Ideal Discrete Signal | |
| |
| |
A Typical Discrete Signal | |
| |
| |
A DFT Window | |
| |
| |
| |
Discrete Time Filtering with MATLAB | |
| |
| |
| |
A Discrete Rectangle | |
| |
| |
| |
A Cosine Test Signal | |
| |
| |
| |
Check Calculation | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
The z-Transform | |
| |
| |
| |
Introduction | |
| |
| |
| |
The z-Transform | |
| |
| |
| |
Fourier Transform, Laplace Transform, z-transform | |
| |
| |
| |
Definition of the z-Transform | |
| |
| |
| |
The z-Plane and the Fourier Transform | |
| |
| |
| |
Calculating the z-Transform | |
| |
| |
| |
Unit Step u[n] | |
| |
| |
| |
Exponential an u[n] | |
| |
| |
| |
Sinusoid cos(n!0) u[n] and sin(n!0) u[n] | |
| |
| |
| |
Differentiation | |
| |
| |
| |
The effect of Sampling Rate | |
| |
| |
| |
A Discrete Time Laplace Transform | |
| |
| |
| |
Properties of the z-Transform | |
| |
| |
| |
z-Transform Pairs | |
| |
| |
| |
Transfer Function of a Discrete Linear System | |
| |
| |
| |
MATLAB Analysis with the z-transform | |
| |
| |
| |
First Order Lowpass Filter | |
| |
| |
| |
Pole-Zero Diagram | |
| |
| |
| |
Bode Plot | |
| |
| |
| |
Impulse Response | |
| |
| |
| |
Calculating Frequency Response | |
| |
| |
| |
Pole Position Determines Frequency Response | |
| |
| |
| |
Digital Filtering - FIR Filter | |
| |
| |
| |
A One Pole FIR Filter | |
| |
| |
| |
A Two Pole FIR Filter | |
| |
| |
| |
Higher Order FIR Filters | |
| |
| |
Frequency Response | |
| |
| |
Pole Zero Diagram | |
| |
| |
Phase Response | |
| |
| |
Step Response | |
| |
| |
| |
Digital Filtering - IIR Filter | |
| |
| |
| |
A One Pole IIR Filter | |
| |
| |
| |
IIR vs FIR | |
| |
| |
| |
Higher Order IIR Filters | |
| |
| |
| |
Combining FIR and IIR Filters | |
| |
| |
| |
Conclusions | |
| |
| |
| |
End of Chapter Exercises | |
| |
| |
| |
Introduction to Communications | |
| |
| |
| |
Introduction | |
| |
| |
| |
A Baseband Signal m(t) | |
| |
| |
| |
The need for a Carrier Signal | |
| |
| |
| |
A Carrier Signal c(t) | |
| |
| |
| |
Modulation Techniques | |
| |
| |
| |
The Radio Spectrum | |
| |
| |
| |
Amplitude Modulation | |
| |
| |
| |
Transmitted Carrier Double Sideband - (AM-TCDSB) | |
| |
| |
| |
Demodulation of AM Signals | |
| |
| |
| |
Graphical Analysis | |
| |
| |
| |
AM Demodulation - Diode Detector | |
| |
| |
| |
Examples of Diode Detection | |
| |
| |
| |
Suppressed Carrier Transmission | |
| |
| |
| |
Demodulation of Single Sideband Signals | |
| |
| |
| |
Percent Modulation and Overmodulation | |
| |
| |
| |
Superheterodyne Receiver | |
| |
| |
| |
An Experiment with Intermediate Frequency | |
| |
| |
| |
When Receivers become Transmitters | |
| |
| |
| |
Image Frequency | |
| |
| |
| |
Beat Frequency Oscillator | |
| |
| |
| |
Digital Communications | |
| |
| |
| |
Modulation Methods | |
| |
| |
| |
Morse Code | |
| |
| |
| |
On O_ Keying (OOK) | |
| |
| |
| |
Bandwidth Considerations | |
| |
| |
| |
Phase Shift Keying | |
| |
| |
| |
Differential Coding | |
| |
| |
| |
Higher-Order Modulation Schemes | |
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Conclusions | |
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End of Chapter Exercises | |
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The Illustrated Fourier Transform | |
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The Illustrated Laplace Transform | |
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The Illustrated z-Transform | |
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MATLAB Reference Guide | |
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Defining Signals | |
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MATLAB Variables | |
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The Time Axis | |
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Common Signals | |
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Non-Periodic | |
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Periodic | |
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Complex Numbers | |
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Plot Commands | |
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Signal Operations | |
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Defining Systems | |
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System Definition | |
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Transfer Function | |
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Zeros and Poles and Gain | |
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State Space Model | |
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Discrete Time Systems | |
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System Analysis | |
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Example System Definition and Test | |
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Reference Tables | |
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Fourier Transform | |
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Fourier Transform Theorems | |
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Laplace Transform | |
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Laplace Transform Theorems | |
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z-Transform | |
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z-Transform Theorems | |