Introduction about Signals and systems

1. Signals & Systems
Course Co ordinator: Dr. R. Sudarmani
1 Department of ECE, Avinshilingam Institute

2. Books
Signals & Systems (Second Edition)  Text book
by
AlanV. Oppenheim,Alan S.Willsky,
S. Hamid Nawab
2 Department of ECE

3. Signal
What is a signal- Information
It is a physical quantity that describes how one parameter is
related to another parameter
Examples:Voltage and Current
The voltage varies with time
t
v
3 Department of ECE

4. •Examples of signal include:
•Electrical signals
•Voltages and currents in a circuit
•Acoustic signals
•Acoustic pressure (sound) over time
•Mechanical signals
•Velocity of a car over time
•Video signals
•Intensity level of a pixel (camera, video) over time
4 Department of ECE

5. Signal
The Speech Signal
Speech due to acoustic pressure
The ECG Signal: the variation of PQRST with time
5 Department of ECE

6. Signal
The image:Two dimentional signal
6 Department of ECE

7. Signal
The image
7 Department of ECE

8. Signal
It is the variation pattern that conveys the information, in a signal
Signal may exist in many forms like acoustic, image, video, electrical,
heat & light signal
8 Department of ECE

9. Example: Signals in an Electrical Circuit
The signals vc and vs are patterns of variation over time
Note, we could also have considered the voltage across the resistor or the current as
signals
+
-
i vcvs
R
C
)(
1
)(
1)(
)(
)(
)()(
)(
tv
RC
tv
RCdt
tdv
dt
tdv
Cti
R
tvtv
ti
sc
c
c
cs
=+
=
−
=
Step (signal) vs at t=1
RC = 1
First order (exponential)
response for vc
vs,vc
t
9 Department of ECE

10. Mathematical Representation
The image is a function of two spatial variables
( )yxs ,
10 Department of ECE

11. Mathematical Representation
A signal can be represented as a function of one or more independent
variables
Examples
( ) ( ) π20sin ≤≤= tttv
( )ts
t
11 Department of ECE

12. Continuous-time signals
A value of signal exists at every instant of time
t
Independent variable
Independent variable
t
12 Department of ECE

13. Discrete-time signals
The value of signal exists only at equally spaced discrete
points in time
Independent variable
Independent variable
t
t
13 Department of ECE

14. Notation
A continuous-time signal is represented by enclosing the
independent variable (time) in parentheses ()
A discrete-time signal is represented by enclosing the
independent variable (index) in square brackets []
( )tx
t
[ ]nx
n14 Department of ECE

15. System
An entity that responds to a signal
Examples
Circuit
systeminput output
15 Department of ECE

16. System
The camera
The Speech Recognition System
Identified
Image
16 Department of ECE

17. System
Block Diagram representation of a system
shows inter-relations of many signals involved in the
implementation of a complex system
System (h(t))
Input Signal
Output Signal
17 Department of ECE

18. How is a System Represented?
A system takes a signal as an input and transforms it into
another signal
In a very broad sense, a system can be represented as the ratio
of the output signal over the input signal
That way, when we “multiply” the system by the input signal, we
get the output signal
System
Input signal
x(t)
Output signal
y(t)
Department of ECE

19. System Response:
Y(t)=x(t)*h(t)
This is called as Convolution
19 Department of ECE

20. Department of ECE20
ThankYou