# Sampling theorem verification

Aim: Verify Sampling theorem.

EQUIPMENTS:

PC with windows (95/98/XP/NT/2000).

MATLAB Software

Sampling Theorem: The sampling theorem specifies the minimum-sampling rate at which a continuous-time signal needs to be uniformly sampled so that the original signal can be completely recovered or reconstructed by these samples alone. This is usually referred to as Shannon's sampling theorem in the literature.

A band-limited signal can be reconstructed exactly if it is sampled at a rate at least twice the maximum frequency component in it.

Program:

``````t=-10:.01:10;
T=4;
fm=1/T;
x=cos(2*pi*fm*t);
subplot(2,2,1);
plot(t,x);
xlabel('time');ylabel('x(t)')
title('continous time signal')
grid;
n1=-4:1:4
fs1=1.6*fm;
fs2=2*fm;
fs3=8*fm;
x1=cos(2*pi*fm/fs1*n1);
subplot(2,2,2);
stem(n1,x1);
xlabel('time');ylabel('x(n)')
title('discrete time signal with fs<2fm')
hold on
subplot(2,2,2);
plot(n1,x1)
grid;
n2=-5:1:5;
x2=cos(2*pi*fm/fs2*n2);
subplot(2,2,3);
stem(n2,x2);
xlabel('time');ylabel('x(n)')
title('discrete time signal with fs=2fm')
hold on
subplot(2,2,3);
plot(n2,x2)
grid;
n3=-20:1:20;
x3=cos(2*pi*fm/fs3*n3);
subplot(2,2,4);
stem(n3,x3);
xlabel('time');ylabel('x(n)')
title('discrete time signal with fs>2fm')
hold on
subplot(2,2,4);
plot(n3,x3)
grid;``````

Output:

Result: In this experiment the sampling theorem have been verified using MATLAB.

Viva Questions:

1. Define Sampling Theorem

Ans: A Band limited signal can be reconstructed exactly if it is sampled at a rate at least twice the maximum signal frequency.

2. Define Nyquist Rate

Ans:Ts=1/fs=1/Sampling frequency=1/2fm

3. Define Energy of a Signal

Ans:A signal x(t) is called an energy signal , if the energy is finite and the power is zero.

4. Define Power of a signal

Ans:A signal x(t) is called an power signal , if the power is finite and the energy is infinite.

5.What is signal band width.

Ans: Bandwidth is the difference between the upper and lower frequencies in a continuous set of frequencies. It is typically measured in hertz, and may sometimes refer to passband bandwidth, sometimes to baseband bandwidth,

6.What is system band width

Ans: Definition of the bandwidth of a system is the frequency range up until the signal's power (at DC) drops by -3dB.

• Created
Dec 09, 2019
• Updated
Mar 03, 2020
• Views
2,440
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