This document provides an overview of signals and systems from the Department of Electronics and Communication Engineering at Avinashilingam Institute. It defines a signal as a physical quantity that describes how one parameter varies with another over time or space. Examples of signals include electrical, acoustic, mechanical, video and image signals. Signals can be represented mathematically as functions of time or other variables and can be continuous or discrete. A system is defined as an entity that responds to a signal, transforming the input signal to an output signal. The relationship between input and output signals of a system can be represented using block diagrams or as the convolution of the input signal with the system's impulse response.

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
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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
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5. Signal
The Speech Signal
Speech due to acoustic pressure
The ECG Signal: the variation of PQRST with time
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6. Signal
The image:Two dimentional signal
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7. Signal
The image
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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
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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
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10. Mathematical Representation
The image is a function of two spatial variables
( )yxs ,
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11. Mathematical Representation
A signal can be represented as a function of one or more independent
variables
Examples
( ) ( ) π20sin ≤≤= tttv
( )ts
t
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12. Continuous-time signals
A value of signal exists at every instant of time
t
Independent variable
Independent variable
t
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13. Discrete-time signals
The value of signal exists only at equally spaced discrete
points in time
Independent variable
Independent variable
t
t
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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
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15. System
An entity that responds to a signal
Examples
Circuit
systeminput output
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16. System
The camera
The Speech Recognition System
Identified
Image
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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
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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)
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19. System Response:
Y(t)=x(t)*h(t)
This is called as Convolution
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20. Department of ECE20
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