• Chapter Objectives
• 1.1 Introduction
• 1.2 Mathematical Modeling of Signals
• 1.3 Continuous-Time Signals
• 1.3.1 Signal operations
• 1.3.2 Basic building blocks for continuous-time signals
• 1.3.3 Impulse decomposition for continuous-time signals
• 1.3.4 Signal classifications
• 1.3.5 Energy and power definitions
• 1.3.6 Symmetry properties
• 1.3.7 Graphical representation of sinusoidal signals using phasors
• 1.4 Discrete-Time Signals
• 1.4.1 Signal operations
• 1.4.2 Basic building blocks for discrete-time signals
• 1.4.3 Impulse decomposition for discrete-time signals
• 1.4.4 Signal classifications
• 1.4.5 Energy and power definitions
• 1.4.6 Symmetry properties
• MATLAB Exercises
• Computing and graphing continuous-time signals
• Describing signals using piecewise linear segments
• Signal operations for continuous-time signals
• Creating periodic signals
• Functions for basic building blocks
• Computing and graphing discrete-time signals
• Periodic extension of a discrete-time signal
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 2.1 Introduction
• 2.2 Linearity and Time Invariance
• 2.2.1 Linearity in continuous-time systems
• 2.2.2 Time invariance in continuous-time systems
• 2.2.3 CTLTI systems
• 2.3 Differential Equations for Continuous-Time Systems
• 2.4 Constant-Coefficient Ordinary Differential Equations
• 2.5 Solving Differential Equations
• 2.5.1 Solution of the first-order differential equation
• 2.5.2 Solution of the general differential equation
• 2.5.3 Finding the natural response of a continuous-time system
• 2.5.4 Finding the forced response of a continuous-time system
• 2.6 Block Diagram Representation of Continuous-Time Systems
• 2.7 Impulse Response and Convolution
• 2.7.1 Finding impulse response of a CTLTI system
• 2.7.2 Convolution operation for CTLTI systems
• 2.8 Causality in Continuous-Time Systems
• 2.9 Stability in Continuous-Time Systems
• 2.10 Approximate Numerical Solution of a Differential Equation
• MATLAB Exercises
• Testing linearity of continuous-time systems
• Testing time invariance of continuous-time systems
• Using linearity to determine the response of the RC circuit
• Numerical solution of the RC circuit using Euler method
• Improved numerical solution of the RC circuit
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 3.1 Introduction
• 3.2 Linearity and Time Invariance
• 3.2.1 Linearity in discrete-time systems
• 3.2.2 Time invariance in discrete-time systems
• 3.2.3 DTLTI systems
• 3.3 Difference Equations for Discrete-Time Systems
• 3.4 Constant-Coefficient Linear Difference Equations
• 3.5 Solving Difference Equations
• 3.5.1 Finding the natural response of a discrete-time system
• 3.5.2 Finding the forced response of a discrete-time system
• 3.6 Block Diagram Representation of Discrete-Time Systems
• 3.7 Impulse Response and Convolution
• 3.7.1 Finding impulse response of a DTLTI system
• 3.7.2 Convolution operation for DTLTI systems
• 3.8 Causality in Discrete-Time Systems
• 3.9 Stability in Discrete-Time Systems
• MATLAB Exercises
• Writing functions for moving average filters
• Testing the functions written in MATLAB Exercise 3.1
• Writing and testing a function for the exponential smoother
• Iteratively solving a difference equation
• Implementing a discrete-time system from its block diagram
• Discrete-time system of MATLAB Exercise 3.5 revisited
• Convolution using MATLAB
• Implementing a moving average filter through convolution
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 4.1 Introduction
• 4.2 Analysis of Periodic Continuous-Time Signals
• 4.2.1 Approximating a periodic signal with trigonometric functions
• 4.2.2 Trigonometric Fourier series (TFS)
• 4.2.3 Exponential Fourier series (EFS)
• 4.2.4 Compact Fourier series (CFS)
• 4.2.5 Existence of Fourier series
• 4.2.6 Gibbs phenomenon
• 4.2.7 Properties of Fourier series
• 4.3 Analysis of Non-Periodic Continuous-Time Signals
• 4.3.1 Fourier transform
• 4.3.2 Existence of Fourier transform
• 4.3.3 Developing further insight
• 4.3.4 Fourier transforms of some signals
• 4.3.5 Properties of the Fourier transform
• 4.3.6 Applying Fourier transform to periodic signals
• 4.4 Energy and Power in the Frequency Domain
• 4.4.1 Parseval’s theorem
• 4.4.2 Energy and power spectral density
• 4.4.3 Autocorrelation
• 4.5 System Function Concept
• 4.6 CTLTI Systems with Periodic Input Signals
• 4.6.1 Response of a CTLTI system to complex exponential signal
• 4.6.2 Response of a CTLTI system to sinusoidal signal
• 4.6.3 Response of a CTLTI system to periodic input signal
• 4.7 CTLTI Systems with Non-Periodic Input Signals
• MATLAB Exercises
• Computing finite-harmonic approximation to pulse train
• Computing multiple approximations to pulse train
• Graphing the line spectrum in Example 4.5
• Line spectrum for Example 4.6
• Graphing system function for RC circuit
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 5.1 Introduction
• 5.2 Analysis of Periodic Discrete-Time Signals
• 5.2.1 Discrete-Time Fourier Series (DTFS)
• 5.2.2 Properties of the DTFS
• 5.3 Analysis of Non-Periodic Discrete-Time Signals
• 5.3.1 Discrete-time Fourier transform (DTFT)
• 5.3.2 Developing further insight
• 5.3.3 Existence of the DTFT
• 5.3.4 DTFT of some signals
• 5.3.5 Properties of the DTFT
• 5.3.6 Applying DTFT to periodic signals
• 5.4 Energy and Power in the Frequency Domain
• 5.4.1 Parseval’s theorem
• 5.4.2 Energy and power spectral density
• 5.4.3 Autocorrelation
• 5.5 System Function Concept
• 5.6 DTLTI Systems with Periodic Input Signals
• 5.6.1 Response of a DTLTI system to complex exponential signal
• 5.6.2 Response of a DTLTI system to sinusoidal signal
• 5.6.3 Response of a DTLTI system to periodic input signal
• 5.7 DTLTI Systems with Non-Periodic Input Signals
• 5.8 Discrete Fourier Transform
• 5.8.1 Relationship of the DFT to the DTFT
• 5.8.3 Properties of the DFT
• 5.8.4 Using the DFT to approximate the EFS coefficients
• 5.8.5 Using the DFT to approximate the continuous Fourier transform
• MATLAB Exercises
• Developing functions to implement DTFS analysis and synthesis
• Testing DTFS functions
• Developing and testing a function to implement periodic convolution
• Steady-state response of DTLTI system to sinusoidal input
• Exploring the relationship between the DFT and the DTFT
• Using the DFT to approximate the DTFT
• Developing functions for circular time shifting and time reversal
• Computing conjugate symmetric and antisymmetric components
• Using the symmetry properties of the DFT
• Circular and linear convolution using the DFT
• Developing a convolution function using the DFT
• Exponential Fourier series approximation using the DFT
• Testing the EFS approximation function
• Fourier transform approximation using DFT
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 6.1 Introduction
• 6.2 Sampling of a Continuous-Time Signal
• 6.2.1 Nyquist sampling criterion
• 6.2.2 DTFT of sampled signal
• 6.2.3 Sampling of sinusoidal signals
• 6.2.4 Practical issues in sampling
• 6.3 Reconstruction of a Signal From Its Sampled Version
• 6.4 Resampling Discrete-Time Signals
• 6.4.1 Reducing the sampling rate by an integer factor
• 6.4.2 Increasing the sampling rate by an integer factor
• MATLAB Exercises
• Spectral relations in impulse sampling
• DTFT of discrete-time signal obtained through sampling
• Sampling a sinusoidal signal
• Natural sampling
• Zero-order hold sampling
• Graphing signals for natural and zero-order hold sampling
• Reconstruction of right-sided exponential
• Frequency spectrum of reconstructed signal
• Resampling discrete-time signals
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 7.1 Introduction
• 7.2 Characteristics of the Region of Convergence
• 7.3 Properties of the Laplace Transform
• 7.3.1 Linearity
• 7.3.2 Time shifting
• 7.3.3 Shifting in the s-domain
• 7.3.4 Scaling in time and s- domains
• 7.3.5 Differentiation in the time domain
• 7.3.6 Differentiation in the s-domain
• 7.3.7 Convolution property
• 7.3.8 Integration property
• 7.4 Inverse Laplace Transform
• 7.4.1 Partial fraction expansion with simple poles
• 7.4.2 Partial fraction expansion with multiple poles
• 7.5 Using the Laplace Transform with CTLTI Systems
• 7.5.1 Relating the system function to the differential equation
• 7.5.2 Response of a CTLTI system to a complex exponential signal
• 7.5.3 Response of a CTLTI system to an exponentially damped sinusoid
• 7.5.4 Pole-zero plot for a system function
• 7.5.5 Graphical interpretation of the pole-zero plot
• 7.5.6 System function and causality
• 7.5.7 System function and stability
• 7.5.8 All-pass systems
• 7.5.9 Inverse systems
• 7.5.10 Bode plots
• 7.6 Simulation Structures for CTLTI Systems
• 7.6.1 Direct-form implementation
• 7.6.2 Cascade and parallel forms
• 7.7 Unilateral Laplace Transform
• 7.7.1 Time shifting
• 7.7.2 Differentiation in time
• 7.7.3 Initial and final value theorems
• MATLAB Exercises
• Three dimensional plot of Laplace transform
• Computing the Fourier transform from the Laplace transform
• Graphing poles and zeros
• Residue calculations
• Symbolic calculations for Laplace transform
• Computing frequency response of a system from pole-zero layout
• Frequency response from pole-zero layout revisited
• System objects
• Bode plots
• Solving a differential equation through Laplace transform
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 8.1 Introduction
• 8.2 Characteristics of the Region of Convergence
• 8.3 Properties of the z-Transform
• 8.3.1 Linearity
• 8.3.2 Time shifting
• 8.3.3 Time reversal
• 8.3.4 Multiplication by an exponential signal
• 8.3.5 Differentiation in the z-domain
• 8.3.6 Convolution property
• 8.3.7 Initial value
• 8.3.8 Correlation property
• 8.3.9 Summation property
• 8.4 Inverse z-Transform
• 8.4.1 Inversion integral
• 8.4.2 Partial fraction expansion
• 8.4.3 Long division
• 8.5 Using the z-Transform with DTLTI Systems
• 8.5.1 Relating the system function to the difference equation
• 8.5.2 Response of a DTLTI system to complex exponential signal
• 8.5.3 Response of a DTLTI system to exponentially damped sinusoid
• 8.5.4 Graphical interpretation of the pole-zero plot
• 8.5.5 System function and causality
• 8.5.6 System function and stability
• 8.5.7 Allpass systems
• 8.5.8 Inverse systems
• 8.6 Implementation Structures for DTLTI Systems
• 8.6.1 Direct-form implementations
• 8.6.2 Cascade and parallel forms
• 8.7 Unilateral z-Transform
• MATLAB Exercises
• Three-dimensional plot of z-transform
• Computing the DTFT from the z-transform
• Graphing poles and zeros
• Using convolution function for polynomial multiplication
• Partial fraction expansion with MATLAB
• Developing a function for long division
• Computing frequency response of a system from pole-zero layout
• Frequency response from pole-zero layout revisited
• Preliminary calculations for a cascade-form block diagram
• Preliminary calculations for a cascade-form block diagram revisited
• Preliminary calculations for a parallel-form block diagram
• Implementing a system using second-order sections
• Solving a difference equation through z-transform
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 9.1 Introduction
• 9.2 State-Space Modeling of Continuous-Time Systems
• 9.2.1 State-space models for CTLTI systems
• 9.2.2 Obtaining state-space model from physical description
• 9.2.3 Obtaining state-space model from differential equation
• 9.2.4 Obtaining state-space model from system function
• 9.2.5 Alternative state-space models
• 9.2.6 CTLTI systems with multiple inputs and/or outputs
• 9.2.7 Solution of state-space model
• 9.2.8 Computation of the state transition matrix
• 9.2.9 Obtaining system function from state-space model
• 9.3 State-Space Modeling of Discrete-Time Systems
• 9.3.1 State-space models for DTLTI systems
• 9.3.2 Obtaining state-space model from difference equation
• 9.3.3 Obtaining state-space model from system function
• 9.3.4 Solution of state-space model
• 9.3.5 Obtaining system function from state-space model
• 9.4 Discretization of Continuous-Time State-Space Model
• MATLAB Exercises
• Obtaining state-space model from system function
• Diagonalizing the state matrix
• Computation of the state transition matrix
• Solving the homogeneous state equation
• Symbolic computation of the state transition matrix
• Obtaining system function from continuous-time state-space model
• Obtaining system function from discrete-time state-space model
• Discretization of state-space model
• Discretization using Euler method
• Problems
• MATLAB Problems
• Chapter Objectives
• 10.1 Introduction
• 10.2 Distortionless Transmission
• 10.3 Ideal Filters
• 10.4 Design of Analog Filters
• 10.4.1 Butterworth lowpass filters
• 10.4.2 Chebyshev lowpass filters
• 10.4.3 Inverse Chebyshev lowpass filters
• 10.4.4 Analog filter transformations
• 10.5 Design of Digital Filters
• 10.5.1 Design of IIR filters
• 10.5.2 Design of FIR filters
• MATLAB Exercises
• Butterworth analog filter design
• Chebyshev polynomials
• Chebyshev type-I analog filter design
• Determining Chebyshev analog filter parameters
• Chebyshev type-II analog filter design
• Lowpass to highpass filter transformation
• Lowpass to bandpass and lowpass to band-reject transformations
• Impulse-invariant design
• IIR filter design using bilinear transformation
• IIR filter design using bilinear transformation revisited
• A complete IIR filter design example
• FIR filter design using Fourier series method
• FIR filter design using Parks-McClellan technique
• Problems
• MATLAB Problems
• MATLAB Projects
• Chapter Objectives
• 11.1 Introduction
• 11.2 The Need for Modulation
• 11.3 Types of Modulation
• 11.4 Amplitude Modulation
• 11.4.1 Frequency spectrum of the AM signal
• 11.4.2 Power balance and modulation efficiency
• 11.4.3 Generation of AM signals
• 11.4.4 Demodulation of AM signals
• 11.5 Double-Sideband Suppressed Carrier Modulation
• 11.5.1 Frequency spectrum of the DSB-SC signal
• 11.6 Single-Sideband Modulation
• MATLAB Exercises
• Compute and graph the AM signal
• EFS spectrum of the tone-modulated AM signal
• Function to simulate a switching modulator
• Testing the switching modulator
• Function to simulate a square-law modulator
• Testing the square-law modulator
• Function to simulate envelope detector
• Testing the envelope detector function
• Problems
• MATLAB Problems
• MATLAB Projects
• A Complex Numbers and Euler’s Formula
• A.1 Introduction
• A.2 Arithmetic with Complex Numbers
• A.2.2 Multiplication and division
• A.3 Euler’s Formula
• B Mathematical Relations
• B.1 Trigonometric Identities
• B.2 Indefinite Integrals
• B.3 Laplace Transform Pairs
• B.4 z-Transform Pairs
• C Closed Forms for Sums of Geometric Series
• C.1 Infinite-Length Geometric Series
• C.2 Finite-Length Geometric Series
• C.3 Finite-Length Geometric Series (Alternative Form)
• D Orthogonality of Basis Functions
• D.1 Orthogonality for Trigonometric Fourier Series
• D.2 Orthogonality for Exponential Fourier Series
• D.3 Orthogonality for Discrete-Time Fourier Series
• E Partial Fraction Expansion
• E.1 Partial Fraction Expansion for Continuous-Time Signals and Systems
• E.2 Partial Fraction Expansion for Discrete-Time Signals and Systems
• F Review of Matrix Algebra