OPERATIONS ON SIGNALS

OPERATIONS ON SIGNALS

1. “OPERATIONS ON SIGNALS”
PREPARED BY :
DISHANT PATEL 140123109009
VISHAL GOHEL 140123109003
JAY PANCHAL 140123109007
MANTHAN PANCHAL 140123109008
GUIDED BY : PROF. HARDIK PATEL

2. Introduction to Signals
•A Signal is the function of one or more
independent variables that carries some
information to represent a physical phenomenon.
•A continuous-time signal, also called an analog
signal, is defined along a continuum of time.

3. Operations of Signals
•Sometime a given mathematical function may
completely describe a signal .
•Different operations are required for different
purposes of arbitrary signals.
•The operations on signals can be
Time Shifting
Time Scaling
Time Inversion or Time Folding

4. x(t ± t
0
) is time shifted version of the signal x(t).
x (t + t
0
) → negative shift
x (t - t
0
) → positive shift




Time Shifting

5. •X(t)X(t+to) Signal Advanced Shift to
the left

6. x(At) is time scaled version of the signal x(t). where A is
always positive.
|A| > 1 → Compression of the signal
|A| < 1 → Expansion of the signal




Time Scaling
Note: u(at) = u(t) time scaling is not applicable for unit
step function.

7. Time scaling Contd.
Example: Given x(t) and we are to find y(t) = x(2t).

The period of x(t) is 2 and the period of y(t) is 1,

8. •Given y(t),
find w(t) = y(3t)
and v(t) = y(t/3).

9. Time Reversal Or Time Folding
•Time reversal is also called time folding
•In Time reversal signal is reversed with
respect to time i.e.
y(t) = x(-t) is obtained for the given
function

11. Amplitude Scaling
C x(t) is a amplitude scaled version of x(t) whose
amplitude is scaled by a factor C.

12. Addition
Addition of two signals is nothing but addition of their
corresponding amplitudes. This can be best
explained by using the following example:
As seen from the diagram above,
-10 < t < -3 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2
-3 < t < 3 amplitude of z(t) = x1(t) + x2(t) = 1 + 2 = 3
3 < t < 10 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2

13. Subtraction
subtraction of two signals is nothing but subtraction of
their corresponding amplitudes. This can be best
explained by the following example:
As seen from the diagram above,
-10 < t < -3 amplitude of z (t) = x1(t) - x2(t) = 0 - 2 = -2
-3 < t < 3 amplitude of z (t) = x1(t) - x2(t) = 1 - 2 = -1
3 < t < 10 amplitude of z (t) = x1(t) + x2(t) = 0 - 2 = -2

14. Multiplication
Here multiplication of amplitude of two or more signals at each instance
of time or any other independent variables is done which are common
between the signals.
Multiplication of signals is illustrated in the diagram below, where X
1
(t)
and X
2
(t) are two time dependent signals, on whom after performing the
multiplication operation we get,
Y(t) = X
1
(t) X
2
(t)

15. 0 0
, an integern n n n® +Time shifting
Operations of Discrete Time
Functions

16. Operations of Discrete Functions
Scaling; Signal Compression
n Kn® K an integer > 1

17. References
Signal and Systems by J. S. Katre
http://electrical4u.com/basic-signal-operations/
http://www.tutorialspoint.com/signals_and_systems/sign
als_basic_operations.htm
http://ocw.mit.edu/courses/electrical-engineering-and-
computer-science/6-01sc-introduction-to-electrical-
engineering-and-computer-science-i-spring-2011/unit-2-
signals-and-systems/designing-control-
systems/MIT6_01SCS11_chap05.pdf
http://in.mathworks.com/

18. THANK YOU