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AIM:To determine the Sampling frequencies (fs) for different signals, Convolving two

signals, Determining stable and unstable systems.

THEORY: Aliasing:

Aliasing refers to an effect that causes different signals to become indistin-guishable from each other when sampled.Aliasing arises when a signal is discretelysampled at a rate that is insufficient to capture the changes in the signal. To avoidaliasing errors ,an analog lowpass filter ,called antialising filter is used.

Different Types of Input:Impulse Input: The impulse function has zero amplitude everywhere except

at t = 0 .At t = 0,the amplitude is infinity such that the area under the curve isequal to one.

x(t) = (t)Unit Step Function: when t in u(t) is less than zero,then the unit step

function is zero,and when t is greater than or equal to zero than the unit stepfunction is unity.

x(t) = u(t)

Even and Odd Signals:Even Signal: An even signal is any signal such that f(t) = f(t). Even

signals are symmetric around the vertical axis.x(t) = cos(t)

Odd Signal: An odd signal, on the other hand, is a signal such thatf(t) = f(t).

x(t) = sin(t)

Linear Convolution and Circular Convolution:

Linear Convolution: Linear convolution is a mathematical operationson two functions f and g ,producing a third function that is the modified version ofone of the original signals giving the area overlap between the two functions.

x(t) = (fg)(t)Circular Convolution: The circular convolution, also known as cyclic

convolution, of two aperiodic functions occurs when one of them is convolved in thenormal way with a periodic summation of the other function.

x(n) = (fgN)[n]

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Causal and Non Causal Systems:Causal System: A causal system is one for which the output at any time

t depends on the present and past inputs but not future inputs.these systems arealso known as non-anticipative systems.

y(t) = x(t) + x(t 1)

Non Causal: A non causal system is one whose output depends onfuture values

y(t) = x(t) + x(t + 3)

System Stability:A system is said to be bounded input and bounded output stable if and

only if every bounded input produces a bounded output.

PROCEDURE:1. Two sin waves with given frequency 1/8 and 7/8 are generated.

2. Stem plots have been generated using stem function and colour coded using colour-fill parameter.

3. we observe that the given sampling frequency undersamples the the signal as fs