Signals and Systems
ELCE 301
Time-domain Analysis of LTI Systems
98
Time-domain Analysis of LTI Systems
Standard procedures in analyzing systems
1.
2.
3.
4.
Identify functionality/equations of the system components.
Choose a model for representing the sys

Signals and Systems
ELCE 301
Continuous-time Systems
72
Continuous-time systems
Basic terminology
Systems process input signals and produce output signals in
order to accomplish a specific task.
Mathematically, a system is described by a functional:
73

Signals and Systems
ELCE 301
Continuous-time Signals
21
Continuous-time signals
Signals as Functions of Time
Continuous-time signals are functions of a real argument
x(t) where time, t, can take any real value
x(t) may be assumed 0 for a given range of t

Signals and Systems
ELCE 301
1
Course Information for Students
General Course Information:
Course Title
Signals and Systems
Course Code
ELCE - 301
Course Instructor
Assoc.Prof. Andrzej Sluzek
andrzej.sluzek@kustar.ac.ae
Phone: 02 501 8578
Office: H 309 H

Signals and Systems
ELCE 301
Advanced analysis of LTI systems
235
Advanced analysis of LTI systems
Block diagrams based on the Laplace transform
integration
derivative
delay
s 2Y (s)
b
k
k
b
sY (s) e2 sY (s) X (s) sX (s)
m
m
m
m
y "(t )
b
k
k
b
y '(t )

Signals and Systems
ELCE 301
Laplace transform in LTI systems
203
Laplace transform in LTI systems
Fundamentals of the Laplace transform
The Laplace transform is similar but NOT the same as the Fourier
transform.
The formal definition:
L[ x(t )] X ( s)
x

Signals and Systems
ELCE 301
Frequency analysis of LTI systems
194
Frequency analysis of LTI systems
Transfer function (frequency response) of an LTI system
Assume an LTI system with the impulse response h(t) (i.e. a response to a
delta input (t) .
The sy

Signals and Systems
ELCE 301
Fourier analysis of continuous-time signals
(part 2)
171
Fourier analysis of continuous-time signals
Fourier transform of CT signals
Assume the same aperiodic function has been periodized in many
different ways.
0 a 2 / 2 1
0

Signals and Systems
ELCE 301
Fourier analysis of continuous-time signals
146
Fourier analysis of continuous-time signals
Fourier series for periodic signals
Let x(t) be periodic with T0 period. Trigonometric Fourier series is
a representation of x(t) as a

Signals and Systems
ELCE 301
Time-domain Analysis of LTI Systems (p.2)
113
Analysis of LTI Systems using inputs
Limitations of ODE-based analysis of LTI systems
1.
Complex systems need complex differential equations (analytic
solution difficult or impossi