bel.m

%Neelabhro Roy
%SNS PROJECT
clear all;
close all;
clc;

% Add extra code for Bandpass filter, Low pass etc.
%Add AWGN and analyse results
f=( 60.*(10^(6)) );
%For the normal input wave of frequency 60MHz
%f=( 60.*(10^(6)) )./ ( 100.*(10^(6)) ) ;                     
% Sampled wave at 100 MHz
t=0:(10^(-8)):0.05;

y=@(t)sin(2*pi*f*t);            
% Making the wave a sine function

d1=0.45*(10^(-6));              
% Time duration for which the wave has non zero amplitude
t=1.45*(10^(-6));               
% Time period (Total time for which a single wave exists) for the whole wave  
fs = 10^8;
x2=0:0.000000000001:1./f;

f=@(x)[y(x).*(0<=x & x<d1)+0.*(d1<=x & x<t)];       
% Division of the wave as per the desired time intervals
pfx2=f(x2);
plot(x2,pfx2);
title('Wave for a single Time Period');
figure;

intvl2=[-2*t 2*t];
z2=linspace(0,t-0.00000001);
fx2 = repmat(f(z2),1,diff(intvl2)/t);               
% Repeats the copies of the arrays for the single wave (generated) to be repeated and appear as a complete wave with multiple clock cycles

x3 = linspace(intvl2(1),intvl2(2),length(fx2));
plot(x3,fx2);
title('The Final Input wave (Continuous Time)');
figure;

stem(x3,fx2);
title('The Final Input wave (Discreet Time)');
% The final input wave or the sampled wave
figure;

%Gaussian White Noise is added to the input signal
N0 = awgn(fx2,10,'measured');
plot(x3,N0);
title(' Plot of the wave with external AWGN ');
figure;



F = fft(fx2);
stem(1./x3,abs(F));
title('Fourier Transform of the Sampled Signal');
figure;

stem(x3,abs(F));
title('Magnitude spectrum of Fourier Transform');
figure;

fc = 40.*(10^(6));

I0 = F .* cos((2.*(pi).*fc).*t); 
plot(1./x3,I0);
title('Wave obtained on multiplying the fft with cos(fc*t), in the frequency domain');
figure;

Q0 = F .* sin((2.*(pi).*fc).*t);
plot(1./x3,Q0);
title('Wave obtained on multiplying the fft with sin(fc*t), in the frequency domain');

%In the following steps we are designing an FIR Filter, through which we
%are going to pass the waves we obtain on getting the sine and cosine
%products of the Fourier Transformed Sampled Sine wave

d = fdesign.lowpass('Fp,Fst,Ap,Ast',0.1,0.15,1,60);
% We are setting the Passband Frequency at 10 MHz and the Stopband
% frequency at 15 MHz and thus, the input arguments of 0.1 and 0.15 in
% lowpass object
designmethods(d);
f = design(d, 'ellip');  
%fvtool(f)   ;                   
Q = filter(f,Q0);
I = filter(f,I0);
stem(1./x3,I);
title('Plot of the fft* with sin wave obtained after filtering, in the frequency domain');
figure;

K = ((I).^2 + (Q).^2);
K1 = log(K);
stem(x3,K); 
title('Plot of the sum of sqaures of the waves obtained after filtering (I^2 + Q^2');
figure;
plot(x3,K1);
title('Plot of log of the sum of sqaures of the waves obtained after filtering log(I^2 + Q^2');