Digital Communication Theory

Consider the signal that is band limited to 50 khz and sample it every 10us. Show graphically that these samples uniquely characterize the waveform.(Use sinusoidal/cosinosoidal waveform).if samples are taken 30us apart instead of 10us ,is it possible to reconstruct the original signal ? Graphically demonstrate that effect using MATLAB.

Solution:

Matlab code

clc;clear all;close all;t=0:.0001/10000:.0001;x=cos(2*pi*50000*t); subplot(3,2,1);plot(t,x);axis([0 0.0001 -1 1]);xlabel('Time');ylabel('Amplitude');title('Cosinusoidal Signal');%sampling every 10u secondsn1=0:0.000001:.0001;x1=cos(2*pi*50000*n1);subplot(3,2,2);stem(n1,x1,'.');axis([0 0.0001 -1 1]);xlabel('Time');ylabel('Amplitude');title('Signal sampled at 10u seconds');%sampling every 30u secondsT2=0.00003;n2=0:0.00003:.0001;x2=cos(2*pi*50000*n2);subplot(3,2,3);stem(n2,x2,'.');axis([0 0.0001 -1 1]);xlabel('Time');ylabel('Amplitude');title('Signal sampled at 30u seconds');%resonstruction of signal sampling every 10u secondssubplot(3,2,4);plot(n1,x1);axis([0 0.0001 -1 1]);xlabel('Time');ylabel('Amplitude');title('Reconstructed Signal when sampled at 10u seconds');%resonstruction of signal sampling every 30u secondssubplot(3,2,5);plot(n2,x2);axis([0 0.0001 -1 1]);xlabel('Time');ylabel('Amplitude');title('Reconstructed Signal when sampled at 30u seconds');

DEPARTMENT OF ELECTRONIC AND COMMUNICATION,BMSCE Page 1

Digital Communication Theory

Output:

Inference:

From the Nyquist Criteria a signal can be reconstructed only when the sampling frequency is greater than twice the message frequency. Signal can be reconstructed only when samples are taken at 10us apart. Reconstruction is not possible when samples are taken at 30us apart.

DEPARTMENT OF ELECTRONIC AND COMMUNICATION,BMSCE Page 2