Fs=4000;
T=1/Fs;
t=(0:230)*T;

x_tx=[zeros(1,100) cos(2*pi*1000*t) zeros(1,100)];

x_rx=[zeros(1,100) cos(2*pi*215*t) zeros(1,100)];

subplot(3,1,1)
h=plot((-100:330)*T/1e-3,x_rx);
set(h,'linewidth',2)
set(gca,'fontsize',12)
xlabel('time (ms)')
ylabel('x_{rx}(t) (v)')
grid


X=fftshift(fft(x_rx,1024));   
% the 128 inside the fft command sets the length after zero-padding 

Omega=(-512:511)*pi/512;  %% DT Frequency... -pi to pi

subplot(3,1,2)
h=stem(Omega/pi,abs(X));
set(h,'linewidth',2)
set(gca,'fontsize',12)
xlabel('\Omega/\pi (Normalized rad/sec)')
ylabel('|X_{rx}[k]|')
grid

f=(Fs/2)*(Omega/pi);   %%%  Convert into equivalent Hz values

subplot(3,1,3)
h=stem(f,abs(X));
set(h,'linewidth',2)
set(gca,'fontsize',12)
xlabel('f  (Hz)')
ylabel('|X_{rx}[k]|')
grid

input('Hit Return to Proceed');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

x_rx_n=x_rx+0.8*randn(size(x_rx));
X_n=fftshift(fft(x_rx_n,1024));

figure

subplot(3,1,1)
h=plot((-100:330)*T/1e-3,x_rx);
set(h,'linewidth',2)
set(gca,'fontsize',12)
xlabel('time (ms)')
ylabel('x_{rx}(t) (v)')
title('Noise-Free Signal in Time Domain')
grid

subplot(3,1,2)
h=plot((-100:330)*T/1e-3,x_rx_n);
set(h,'linewidth',2)
set(gca,'fontsize',12)
xlabel('time (ms)')
ylabel('x_{rx}(t) (v)')
title('Noisy Signal in Time Domain')
grid

subplot(3,1,3)
h=stem(f,abs(X_n));
set(h,'linewidth',2)
set(gca,'fontsize',12)
xlabel('f  (Hz)')
ylabel('|X_{rx}[k]|')
title('DFT of Noisy Signal')
grid