ECE 3500 Fundamentals of Signals and Systems (Fall 2019)
Part I: Language of Signals and Systems
Syllabus
Motivations and Basic Concepts
What are the signals and systems?
Application of signals and systems?
What we will learn in ECE 3500?
What follows this class?
Typs of Signals
Engery and Power of Signals
References:
Lathi's book: Ch. 1.11.2, 1.5, 8.1, 8.4
Mitra's book: Ch. 1.11.2, 1.41.5, 3.1, 7.17.2
Engery and Power of Signals
Basic Signal Operations
Introduction to Periodic Signals
References:
Lathi's book: Ch. 1.11.3, 1.5, 8.1, 8.4
Mitra's book: Ch. 3.13.4, 7.17.4
Periodic Signals
References:
Lathi's book: Ch. 1.2, 1.4, 8.2, B.1
Mitra's book: Ch. 3.13.4, 7.17.4
Complex Numbers
Specific Signals
Complex Exponentials
Refrences:
Lathi's book: Ch. B.1, 1.4, 8.2
Mitra's book: Ch. 2.12.5, 3.2, 7.3
Specific Signals
Unit Impluse Signals
Unit Step Signals
Refrences:
Lathi's book: Ch. 1.4, 8.2
Mitra's book: Ch. 3.2, 7.3
System Properties
Refrences:
Lti's book: Ch. 1.61.7, 2.6
Mitra's book: Ch. 4.14.3, 8.18.4
System Properties Cont.
Convolution Integral/Sum
Refrences:
Lathi's book: Ch. 1.61.7, 2.6, 2.12.5, 9.19.5
Mitra's book: Ch. 4.14.3, 8.18.4
Convolution Examples (Continuoustime)
Refrences:
Lathi's book: Ch. 2.12.5, 9.19.5
Mitra's book: Ch. 4.14.3, 8.18.4
Convolution Examples (Discretetime)
Convolution Properties
Properties of LTI systems using unit impluse response
Refrences:
Lathi's book: Ch. 2.12.5, 9.19.5
Mitra's book: Ch. 4.14.3, 8.18.4
Part II: Continoustime Signals and Systems
Frequency Basis and Fourier Series (FS)
Cosine and Sine Fourier Series
Complex Exponential Fourier Series
Examples of Complex Exponential Fourier Series
Drichlet Conditions
Properties of Fourier Series
Continuoustime Fourier Transform
Magnitude and Phase of CTFT
Uniform Convergence Conditions (Dirichlet Conditions)
Uniform Convergence Conditions (examples)
Properties of CTFT
Properties of CTFT
Applications: Amplitude Modulations (AM)
Laplace Transform
Inverse Laplace Transform
Applications of Laplace Transform: Determine System Properties (causal and BIBO stable), Analog Filter Design
Refrences:
Lathi's book: Ch. 6.7, 7.17.2
Mitra's book: Ch. 5.75.9, 6.16.4
Part III: Discretetime Signals and Systems
Review of Part II
Sampling
Nyquest Sampling Theorem and Aliasing
Refrences:
Lathi's book: Ch. 5.15.2, 8.3
Mitra's book: Ch.7.1, 7.5
Sampling
Nyquest Sampling Theorem and Aliasing
AntiAliasing Filter
Refrences:
Lathi's book: Ch. 5.15.2, 8.3
Mitra's book: Ch.7.1, 7.5
Examples:
Homework 8: here.
DiscreteTime Fourier Transform (DFT)
DTFT Properties
DTFT Applications
DTFT Existence Conditions
ZTransform
Refrences:
Lathi's book: Ch. 10.110.4, 11.111.3
Mitra's book: Ch.9.29.3, 9.8
Examples:
ZTransform Examples
Inverse ZTransform
Applications of ZTransform
Resampling (Downsampling, Upsampling)
Refrences:
Lathi's book: 8.4, 10.4
Mitra's book: None.
Homework 10 solutions: here.
Homework 11: here.
Homework 11 solutions: here.
Midterm 3 solutions: here.
