OPERATIONS ON SIGNALS

“OPERATIONS ON SIGNALS”

PREPARED BY :

DISHANT PATEL 140123109009VISHAL GOHEL 140123109003

JAY PANCHAL 140123109007

MANTHAN PANCHAL 140123109008

GUIDED BY : PROF. HARDIK PATEL

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.

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

x(t ± t0) is time shifted version of the signal x(t).

x (t + t0) → negative shift

x (t - t0) → positive shift

Time Shifting

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

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.

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,

• Given y(t),

find w(t) = y(3t)

and v(t) = y(t/3).

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

Amplitude Scaling

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

AdditionAddition 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 = 33 < t < 10 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2

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 = -13 < t < 10 amplitude of z (t) = x1(t) + x2(t) = 0 - 2 = -2

MultiplicationHere 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 X1(t) and X2(t) are two time dependent signals, on whom after performing the multiplication operation we get, Y(t) = X1(t) X2(t)

0 0 , an integern n n n Time shifting

Operations of Discrete Time Functions

Operations of Discrete Functions

Scaling; Signal Compressionn Kn K an integer > 1

ReferencesSignal and Systems by J. S. Katre

http://electrical4u.com/basic-signal-operations/

http://www.tutorialspoint.com/signals_and_systems/signals_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/

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