Contents of the course
Classification
of Signals and Basic Signal Properties. Some MATLAB Examples.
Time Domain Models of Linear Time Invariant (LTI) Systems:
Continuous time systems. Basic
system properties. Causal LTI systems described by differential
equations. System block diagrams. The solutions of differential
equations. The unit impulse response and convolution integral. State
variable analysis of LTI systems. Discrete time systems. Difference
equations. The unit sample response and discrete convolution.
Frequency Domain Models of LTI Sytems:
Fourier series representation of continuous-time and discrete- time
periodic signals. The continuous-time and discrete-time Fourier transform. Discrete
Fourier transform. Time and frequency characterization of signals
and systems. Frequency-domain analysis of systems.
The Laplace Transform and s-Domain Models of LTI
Systems:
Definition of the two-sided (bilateral) and one-sided (unilateral)
Laplace transform. Inverse Laplace transform and contour integration.
Impulse response and convolution. S-domain analysis of LTI
differential systems. Pole-zero plot. Stability analysis.
The
z-Transform and z-Domain Models of LTI Systems.
z-transform
and inverse z-transform. Region of convergence of the z-transform.
z-domain analysis of discrete LTI systems.
LTI
Systems With Random Inputs: Introduction to random
process. Definition of Random
variables,stochastic process, first and
second order
statistics, moment, correlation and co-variance,
stationary process, ergodicity. System resonse.
Objectives of the Course
The
objectives of this course are to provide students with a basic
understanding of signals and systems properties, and ability of
modeling-analysis of linear time invariant (LTI) systems using time
and frequency domain approaches such as differential equations, unit
impulse response, state-variable, Fourier series and Fourier
transforms, transfer function, Laplace transform and z-transform.
These topics
of study will be the basis for later courses in communications,
digital signal processing and control theory. Students will
confirmate of their theoretical knowledge by computer simulations
using MATLAB.
Year/Semester:
2nd
year Fall Semester for E&E Eng, 2nd year Spring Semester
for Computers Eng.
Status: Compulsory
Department:
Electrical and
Electronics Engineering (ELK207)
Computers Engineering (BIL202)
Prerequisite/Recommended:
None
Form of Teaching:
Lectures (56
Hours)- 4 hours per week (E&E Eng)
Lectures (42 Hours)- 3 hours per week (C Eng)
Lecturer:
Assist.
Prof. Dr. Ali Gangal
Language of instruction: Turkish
Lesson Hours: Tuesday 09-12
(Computers Eng 2005 2006 Spring Semester)
Textbook/Material:
Power point
presentation
Lecture notes:
To be delivered during the lectures.
Method of assessment:
A
written midterm exam (30%), quizzes and practical homeworks (20%)
and a written end-of-term exam (50%)
Make-up Policy
Only one make-up examination will be given to those who miss any of
the midterms or the final. The student who wishes to take the make-up
exam must provide a valid excuse after the missed exam.
NG Policy
NG grade will be given to students who do not attend more than 70%
of the course lecture hours, miss the exams and fail.
Course Outline
1. Classification of Signals and Basic Signal
Properties
Continuous-Time
and Discrete-Time Signals. Periodic and Aperiodic Signals. Energy
and Power Signals. L’Hopital’s Rule.
Deterministic and Random Signals.
Exponential and Sinusoidal Signals, Euler’s Formula. The Sampling
Theorem: Shannon’s Sampling Theory, Nyquist Rate. Sampling of
Sinusoidal Signals. The Effect of Undersampling: Aliasing.
Symmetricity. Even and Odd Functions. Even and Odd Components of a
Signal. Some Useful Signal Operations: Time-Shifting, Time Scaling,
Time Inversion, Combined Operations. Singular Functions: Unit
Impulse, Unit Step and Unit Ramp Functions. Representation of a
Signal by Singular Functions. Mathematical Description of a Signal
From Its Sketch. Orthogonal and Orthonormal Signals. Representation
of a Signal by Orthogonal Functions. The Gram-Schmidt Algorithm. Discrete Time Processing of
Continuous-Time Signals. Sketching of Signals Using MATLAB. Some
MATLAB Examples.
2. Time Domain Models of Continuous Time Systems
Basic System
Properties: linearity, causality, stability, memory, invertibility,
time-invariance. Causal LTI Systems Described by Differential
Equations. System Block Diagrams. The Solutions of Differential
Equations: 1-Homogenous and Particular Solution, 2-The Zero-Input
and The Zero-State Solution. The Unit
Impulse Response, The Convolution Integral. Graphical Understanding
of Convolution. Circular Convolution. Converting a Differential
Equation to State Variable Equations. State Variable Analysis of LTI
Systems. The Cayley-Hamilton Theorem. Difference Equations. Initial Conditions and Iterative
Solution of Linear Difference Equations. The Unit Sample Response,
Discrete Convolution, Discrete Circular Convolution. Some MATLAB
Examples.
3.
Frequency Domain Models of LTI Sytems
Fourier Series Representation of Continuous-Time
Periodic Signals:
Trigonometric Fourier Series, The Gibbs Phenomenon. Exponential Fourier Series. Properties
of Continuous-Time Fourier Series. Representation
of Aperiodic Signals: The Continuous-Time Fourier Transform. The
Fourier Transform for Periodic Signals. Properties of the Continuous-Time
Fourier Transform. Parseval's Theorem. Tables of Fourier Properties and Basic Fourier Transform Pairs.
Systems Characterized by Linear Constant-Coefficient Differential
Equations.
Fourier Series Representation of Discrete-Time Periodic Signals:
Discrete-Time Fourier Series. Properties of Discrete-Time Fourier
Series.
The
Discrete-Time Fourier Transform.
Representation of Aperiodic
Signals: The Discrete-Time Fourier Transform. The Fourier Transform
for Periodic Signals. Properties of the Discrete-Time Fourier
Transform. Tables of Fourier Transform Properties and Basic Fourier
Transform Pairs. Duality. Systems Characterized by Linear
Constant-Coefficient Difference Equations.
Time and
Frequency Characterization of Signals and Systems.
The
Magnitude-Phase Representation of the Fourier Transform. The
Magnitude-Phase Representation of the Frequency Response of LTI
Systems. Time-Domain Properties of Ideal Frequency-Selective
Filters. Time-Domain and Frequency-Domain Aspects of Nonideal
Filters. Examples of Time- and Frequency-Domain Analysis of Systems.
Some MATLAB Examples.
4. S-Domain Models of Continuous Time Systems
Definition
of the two-sided (Bilateral) Laplace transform and its relation to
the continuous-time Fourier transform. Region of convergence of the
two-sided Laplace transform. Inverse Laplace transform and contour
integration. Properties of the two-sided Laplace transform.
Definition and properties of the one-sided (Unilateral) Laplace
transform. Some Laplace Transform Pairs. Initial value theorem,
final value theorem. Impulse response,
convolution and the system function characterization of continuous-time
LTI systems. LTI differential systems, rational system functions,
causality and stability criteria. Block diagram representation.
Transient and steady-state response of LTI differential systems.
Forced and natural response of LTI differential system with nonzero
initial conditions. Pole-zero Plot. Stability Analysis, Routh-Hurwitz
Stability Criterion. MATLAB Examples.
5. The Z-Transform and Z-Domain Models of LTI
Systems
The z-Transform.
The Region of Convergence for the z-Transform. The Inverse
z-Transform. Geometric Evaluation of the Fourier Transform from
the Pole-Zero Plot. Properties of the z-Transform. Some
Common z-Transform Pairs. Analysis and Characterization of
LTI Systems Using z-Transforms. System Function Algebra and
Block Diagram Representations. The Unilateral z-Transforms.
MATLAB Examples.
6.
LTI Systems With Random Inputs
Introduction, discrete time random process. Random variables,
Stochastic process, first, second order statistics, moment,
correlation and co-variance stationary process, ergodicity. MATLAB
Examples.
|
