Principles of Signals and Systems

Preface
Contents
Abbreviations
Chapter 1: Introduction to Signals and Systems
	1.1 System
Chapter 2: Basic Signal Functions and Their Manipulations
	2.1 Continuous-Time Signals
	2.2 Discrete-Time Signals
	2.3 Manipulation of Signals
		2.3.1 Manipulation of Continuous-Time Signals
			Manipulation of Periodic Signals (Functions)
		2.3.2 Manipulation of Digital Signals
	2.4 Sampling
	2.5 Basic Signals Used in Communication and Signal Processing
		2.5.1 Representation of Signals with Mathematical Functions
		2.5.2 Continuous-Time Basic Signal Functions
			Unit Step Function
			Unit Delta Step Function
			Unit Delta Impulse Function
			Unit Impulse Function
		2.5.3 Properties of the Impulse Function
			Ramp Function
			Exponential Function
			Sinusoidal Function
			Exponentially Damped Sinusoidal Function
			Complex Exponential Function
		2.5.4 Basic Digital Signal Functions
			Unit Step Function
			Unit Impulse Function
			Ramp Function
			Digital Exponential Function
	2.6 Electronic Circuits Used in Signal Generation
		2.6.1 Passive Circuit Elements
			Inductor
			Capacitor
			Resistor
			Unit Step Function
			Impulse Function
			Sinusoidal Function
		2.6.2 Exponential Function
		2.6.3 Exponentially Damped Sinusoidal Function
		2.6.4 Linear and Time-Invariant Systems
		2.6.5 Representation of Linear and Time-Invariant System with Differential Equations
	Problems
Chapter 3: Energy, Power, Convolution, and Systems
	3.1 Energy and Power in Signals
		3.1.1 Energy and Power in Continuous-Time Signals
			Instantaneous Power
			Total Energy
			Average Power
		3.1.2 Energies and Powers of Discrete-Time Signals
			Instantaneous Power
			Total Energy
			Average Power
	3.2 Convolution
		3.2.1 Convolution of Continuous-Time Signals
		3.2.2 Impulse Function and Convolution
		3.2.3 Convolution of Digital Signals
		3.2.4 Convolution of Digital Signals
		3.2.5 Digital Impulse Signal (Function) and Convolution Operation
	3.3 Systems and Their Features
		3.3.1 Mathematical Expressions of the Systems
		3.3.2 Causality
		3.3.3 Memory
		3.3.4 Stability
		3.3.5 Invertibility
		3.3.6 Linearity
		3.3.7 Time Invariance
		3.3.8 Time Domain Representations of Linear and Time-Invariant Systems
		3.3.9 The Relationship Between Impulse and Unit Step Responses of a Linear and Time-Invariant System
		3.3.10 The Response of a Linear and Time-Invariant System to an Exponential Signal
		3.3.11 Determining the Properties of a Linear and Time-Invariant System from Impulse Response
			Memory
			Causality
			Stability
		3.3.12 Representation of Linear and Time-Invariant Systems with Differential and Difference Equations
			Continuous-Time Systems
			Digital Systems
		3.3.13 Solving Differential and Difference Equations of Linear and Time-Invariant Systems
			Differential Equation Solution
			Solving Difference Equations
	Problems
Chapter 4: Fourier Analysis of Continuous-Time Signals
	4.1 Fourier Series Representations of Continuous-Time Periodic Signals
	4.2 Fourier Integral and Fourier Transform
		4.2.1 Fourier Cosine and Sine Transforms
		4.2.2 Fourier Transform
	Summary
	Problems
Chapter 5: Fourier Analysis of Digital Signals
	5.1 Fourier Series Representations of Digital Signals
		5.1.1 Periodic Digital Signal
		5.1.2 Fourier Series Representations of Digital Signals
		5.1.3 Properties for the Fourier Series Representation of Discrete-Time Periodic Signals (Digital Signals)
		5.1.4 Convolution of Periodic Digital Signals
	5.2 Fourier Transform of Digital Signals
		5.2.1 Fourier Transform of Digital Periodic Signals
		5.2.2 Properties of the Fourier Transform
	Summary
	Problems
Chapter 6: Laplace Transform
	6.1 Laplace Transform
		6.1.1 Convergence Region
	6.2 Inverse Laplace Transform
	6.3 Laplace Transforms of Derivatives and Integrals of Functions
	Summary
	Problems
Chapter 7: Z Transform
	7.1  Transform
		7.1.1 Properties of the Convergence Region
	7.2 Inverse  Transform
	7.3 Z Transform of Linear and Time-Invariant Digital Systems
	7.4 Solving the Discrete-Time Difference Equations of Causal Systems Using Z Transform
	Summary
	Problems
Chapter 8: Practical Applications
	8.1 Computational Complexity of the Discrete Fourier Transform Algorithm and Complexity Reduction
	8.2 GoertzelAlgorithm
	8.3 Dual-Tone Multi-frequency (DTMF) Detection Using Goertzel Algorithm
	8.4 Fast Fourier Transform (FFT)
Appendix A: Frequently Used Mathematical Expressions
Appendix B: Fourier, Laplace, and Z Transform Pairs
Bibliography
Index