Signals & Systems For Dummies®
Visit www.dummies.com/cheatsheet/signalsandsystems to view this book's cheat sheet.
Table of Contents
Part I: Getting Started with Signals and Systems
Part II: Exploring the Time Domain
Part III: Picking Up the Frequency Domain
Part IV: Entering the s- and z-Domains
Part I: Getting Started with Signals and Systems
Chapter 1: Introducing Signals and Systems
Getting Mixed Signals . . . and Systems
Working in spurts: Discrete-time signals and systems
Signals and Systems in Other Domains
Viewing signals in the frequency domain
Traveling to the s- or z-domain and back
Testing Product Concepts with Behavioral Level Modeling
Staying abstract to generate ideas
Exploring Familiar Signals and Systems
Using Computer Tools for Modeling and Simulation
Chapter 2: Brushing Up on Math
Revealing Unknowns with Algebra
Checking solutions with computer tools
Exploring partial fraction expansion
Making Nice Signal Models with Trig Functions
Manipulating Numbers: Essential Complex Arithmetic
Believing in imaginary numbers
Applying the phasor addition formula
Chapter 3: Continuous-Time Signals and Systems
Exponential and sinusoidal signals
Singularity and other special signal types
Getting Hip to Signal Classifications
Putting it together: Shift and flip
Checking Out System Properties
Time-invariant and time varying
Choosing Linear and Time-Invariant Systems
Chapter 4: Discrete-Time Signals and Systems
Exponential and sinusoidal signals
Surveying Signal Classifications in the Discrete-Time World
Deterministic and random signals
Recognizing energy and power signals
Computer Processing: Capturing Real Signals in Discrete-Time
Capturing and reading a wav file
Classifying Systems in Discrete-Time
Part II: Exploring the Time Domain
Chapter 5: Continuous-Time LTI Systems and the Convolution Integral
Establishing a General Input/Output Relationship
LTI systems and the impulse response
Developing the convolution integral
Looking at useful convolution integral properties
Working with the Convolution Integral
Seeing the general solution first
Solving problems with finite extent signals
Dealing with semi-infinite limits
Step response from impulse response
Causality and the impulse response
Chapter 6: Discrete-Time LTI Systems and the Convolution Sum
Specializing the Input/Output Relationship
Using LTI systems and the impulse response (sequence)
Getting to the convolution sum
Simplifying with Convolution Sum Properties and Techniques
Applying commutative, associative, and distributive properties
Convolving with the impulse function
Solving convolution of finite duration sequences
Working with the Convolution Sum
Using spreadsheets and a tabular approach
Attacking the sum directly with geometric series
Connecting the step response and impulse response
Chapter 7: LTI System Differential and Difference Equations in the Time Domain
Introducing the general Nth-order system
Considering sinusoidal outputs in steady state
Finding the frequency response in general Nth-order LCC differential equations
Checking out the Difference Equations
Modeling a system using a general Nth-order LCC difference equation
Using recursion to find the impulse response of a first-order system
Considering sinusoidal outputs in steady state
Solving for the general Nth-order LCC difference equation frequency response
Part III: Picking Up the Frequency Domain
Chapter 8: Line Spectra and Fourier Series of Periodic Continuous-Time Signals
Sinusoids in the Frequency Domain
Viewing signals from the amplitude, phase, and frequency parameters
Forming magnitude and phase line spectra plots
Working with symmetry properties for real signals
Exploring spectral occupancy and shared resources
Establishing a sum of sinusoids: Periodic and aperiodic
General Periodic Signals: The Fourier Series Representation
Analysis: Finding the coefficients
Synthesis: Returning to a general periodic signal, almost
Checking out waveform examples
Working problems with coefficient formulas and properties
Chapter 9: The Fourier Transform for Continuous-Time Signals and Systems
Tapping into the Frequency Domain for Aperiodic Energy Signals
Working with the Fourier series
Using the Fourier transform and its inverse
Getting amplitude and phase spectra
Seeing the symmetry properties for real signals
Finding energy spectral density with Parseval’s theorem
Applying Fourier transform theorems
Getting Around the Rules with Fourier Transforms in the Limit
Handling singularity functions
Unifying the spectral view with periodic signals
LTI Systems in the Frequency Domain
Checking out the frequency response
Evaluating properties of the frequency response
Getting connected with cascade and parallel systems
Seeing the Need for Sampling Theory
Periodic Sampling of a Signal: The ADC
Analyzing the Impact of Quantization Errors in the ADC
Analyzing Signals in the Frequency Domain
Impulse train to impulse train Fourier transform theorem
Finding the spectrum of a sampled bandlimited signal
Aliasing and the folded spectrum
Applying the Low-Pass Sampling Theorem
Reconstructing a Bandlimited Signal from Its Samples: The DAC
Interpolating with an ideal low-pass filter
Using a realizable low-pass filter for interpolation
Chapter 11: The Discrete-Time Fourier Transform for Discrete-Time Signals
Relating the continuous-time spectrum to the discrete-time spectrum
Getting even (or odd) symmetry properties for real signals
Studying transform theorems and pairs
Getting mean-square convergence
Finding Fourier transforms in the limit
LTI Systems in the Frequency Domain
Taking Advantage of the Convolution Theorem
Chapter 12: The Discrete Fourier Transform and Fast Fourier Transform Algorithms
Establishing the Discrete Fourier Transform
Computing the DFT with the Fast Fourier Transform
Decimation-in-time FFT algorithm
Application Example: Transform Domain Filtering
Making circular convolution perform linear convolution
Using overlap and add to continuously filter sequences
Part IV: Entering the s- and z-Domains
Chapter 13: The Laplace Transform for Continuous-Time
Seeing Double: The Two-Sided Laplace Transform
Finding direction with the ROC
Checking stability for LTI systems with the ROC
Checking stability of causal systems through pole positions
Digging into the One-Sided Laplace Transform
Getting Back to the Time Domain
Working double time with twin poles
Using tables to complete the inverse Laplace transform
Working with the System Function
Managing nonzero initial conditions
Checking the frequency response with pole-zero location
Chapter 14: The z-Transform for Discrete-Time Signals
The ROC and stability for LTI systems
Using the table-lookup approach
Surveying z-Transform Properties
Leveraging the System Function
Applying the convolution theorem
Finding the frequency response with pole-zero geometry
Chapter 15: Putting It All Together: Analysis and Modeling Across Domains
Using PyLab for LCC Differential and Difference Equations
Mashing Domains in Real-World Cases
Problem 1: Analog filter design with a twist
Problem 2: Solving the DAC ZOH droop problem in the z-domain
Chapter 16: More Than Ten Common Mistakes to Avoid When Solving Problems
Miscalculating the Folding Frequency
Getting Confused about Causality
Plotting Errors in Sinusoid Amplitude Spectra
Being Unfamiliar with Calculator Functions
Ignoring the Convolution Output Interval
Forgetting to Reduce the Numerator Order before Partial Fractions
Forgetting about Poles and Zeros from H(z)
Disregarding the Action of the Unit Step in Convolution
Chapter 17: Ten Properties You Never Want to Forget
Convolution with Impulse Functions
Frequency Samples of N-point DFT
Integrator and Accumulator Unstable