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 minimumsampling rate at which a continuoustime 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 bandlimited 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.

UpdatedMar 03, 2020

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