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Author: VivekKrG

Assignment/High_Pass_Filter.slx

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+%************ASSIGNMENT******************
+% Problem 1
+%Create a 10x10 random matrix with the command A=rand(10). Now do the following operations. 
+%   a) Multiply all elements by 100 and then round off all elements of the matrix to integers with the command A=fix(A). 
+%   b) Replace all elements of A<10 with Zeros.
+%   c) Replace all elements of A>90 with infinity (inf). 
+%   d) Extract all 30 <= aij <= 50 in a vector b, that is find all elements between 30 and 50 and put them in a vector b. 
+%
+A=rand(10);
+%%
+%(a)
+A=A*100;
+A=fix(A);
+%%
+%(b)
+A(A<10)=0;
+%%
+%(c)
+A(A>90)=inf;
+%%
+%(d)
+b=A(A>=30 & A<=50)
+
+

Assignment/Low_Pass_Filter.slx

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+% ****************ASSIGNMENT****************
+% 2. Find out the values of current il. 12 13 for the following given ckt using the
+%    MATLAB R1=5 ohm, R2=100 ohm, R3=200 ohm,R4=150 ohm,R=250 ohm; V1= 5V and V2= 10V.
+%                 [V]= [R][I]
+%                 [i]= inv([R])[V]
+%                 -V1= (R1+R4)I1 + (-R4)I2      + (0)I3
+%                   0= (-R4)I1   + (R2+R4+R5)I2 + (-R5)I3
+%                 -V2= (0)I1     + (-R5)I2      + (R3+R5)I3
+R1=5;
+R2=100;
+R3=200;
+R4=150;
+R5=250;
+V1=5;
+V2=10;
+V=[-V1;0;-V2];
+R=[R1+R4 -R4       0;
+   -R4   R2+R4+R5 -R5;
+   0     -R5      R3+R5];
+I=inv(R)*V;
+I

Assignment/Q1.m

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+% *********ASSIGNMENT*********************
+% 3. Write a program which does the following operation on given signal:
+%     a) Addition, Multiplication and Convolution of two signal
+%     b) Folding, Shifting and Scaling operation on a given signal 
+%%
+%Let two DIGITAL signals are X, Y
+N=0:9;
+X=N;
+H=fliplr(N);%H=9:-1:0
+subplot(421); stem(N,X,'r'); title('Signals X');
+subplot(422); stem(N,H,'g'); title('Signals Y');
+%%
+%(a)Addition, Multiplication and Convolution
+Added=X+H;
+Product=X.*H;
+Convolution=conv(X,H);
+subplot(423); stem(N,Added,'b'); title('Added signals');
+subplot(424); stem(N,Product,'m'); title('Product signals');
+subplot(425); stem(-9:9,Convolution,'r'); title('Convolution signals');
+%stem(0:19,Convolution)
+%%
+%(b) Folding, Shifting and Scaling operation on a given signal
+%Folding using inbuilt function
+Folded1=fliplr(X);
+%Using for loop
+Folded2=[];
+for ij=length(X):-1:1
+    Folded2=[Folded2  X(ij)];
+end
+subplot(426); stem(0:9,Folded2,'r'); title('Folded signals');
+%Shifing by 3 in right(Delay)
+N2=N+3;
+Shfited1(N2)=X;
+subplot(427); stem(0:11,Shfited1,'r'); title('Shifted signals');
+%Scaling by factor c=2
+Scaled=X(1:2:9);
+subplot(428); stem(0:4,Scaled,'r'); title('Scaled signals');

Assignment/Q2.m

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+%%
+%   Q4. Program to draw fourier transform of trinangular function.
+T=4;    %a= -2 to b= +2
+V0=5;   %V=+-(10) Asussumed 
+w= 2*pi/T;
+%%
+%Function declareation
+fun1= @(t)( (-4*V0/T).*(t + T/2) );
+fun2= @(t)( (4*V0/T).*t );
+fun3= @(t)( (-4*V0/T).*(t - T/2) );
+func= @(t)( fun1(t)+fun2(t)+fun3(t) );
+%%
+%a0, an & bn finding
+a10=@(n)(2/T)*integral( fun1, -T/2, -T/4 );
+a20=@(n)(2/T)*integral( fun2, -T/4,  T/4 );
+a30=@(n)(2/T)*integral( fun3,  T/4,  T/2 );
+a0 =@(n)( a10(n)+a20(n)+a30(n) );
+
+a1n=@(n)(2/T)*integral( @(t)fun1(t).*cos(n*w*t), -T/2, -T/4 );
+a2n=@(n)(2/T)*integral( @(t)fun2(t).*cos(n*w*t), -T/4,  T/4 );
+a3n=@(n)(2/T)*integral( @(t)fun3(t).*cos(n*w*t),  T/4,  T/2 );
+an =@(n)( a10(n)+a20(n)+a30(n) );
+
+b1n=@(n)(2/T)*integral( @(t)fun1(t).*sin(n*w*t), -T/2, -T/4 );
+b2n=@(n)(2/T)*integral( @(t)fun2(t).*sin(n*w*t), -T/4,  T/4 );
+b3n=@(n)(2/T)*integral( @(t)fun3(t).*sin(n*w*t),  T/4,  T/2 );
+bn =@(n)( b1n(n)+b2n(n)+b3n(n) );
+%%
+t=-4:0.01:4;
+t1=-3:0.01:-1;
+t2=-1:0.01: 1;
+t3= 1:0.01: 3;
+%%
+for j=1:2:50
+    
+    %hold on
+    plot(t1,fun1(t1),'k')
+    plot(t2,fun2(t2),'k')
+    plot(t3,fun3(t3),'k')
+    
+    FS=0;
+    for k=1:j
+        FS=FS + an(k).*cos(k*w*t)+bn(k).*sin(k*w*t);
+    end
+    FS=FS+a0(0);
+    plot(t,t==0,'g',t==0,t,'g', t1,fun1(t1),'b', t2,fun2(t2),'b', t3, fun3(t3),'b',t,FS,'r' )
+    pause(1)
+end

Assignment/Q3.m

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+%%
+%Amplitude modulation
+
+Ac=2;      fc=300;
+%mu=input('Enter Value of mu: ');      
+%Am= mu*Ac;  
+fm=25;
+
+mt= @(t)sin(2*pi*fm*t);
+ct= @(t)sin(2*pi*fc*t);
+yt= @(t,mu)Ac*(1 + mu*mt(t)).*ct(t);
+
+t=0:0.0001:0.1;
+subplot(5,1,1)
+plot( t,mt(t),'g' );
+title('Message Signal: m(t)');
+xlabel('time'); ylabel('Amplitude');
+
+subplot(5,1,2)
+plot( t,2*ct(t),'b' );
+title('Career Signal: c(t)');
+xlabel('time'); ylabel('Amplitude');
+
+subplot(5,1,3)
+plot( t,yt(t,0.5),'r' );
+title('Amplitude Modulated Signal: y(t): mu=0.5');
+xlabel('time'); ylabel('Amplitude');
+
+subplot(5,1,4)
+plot( t,yt(t,1),'r' );
+title('Amplitude Modulated Signal: y(t): mu=1');
+xlabel('time'); ylabel('Amplitude');
+
+subplot(5,1,5)
+plot( t,yt(t,1.5),'r' );
+title('Amplitude Modulated Signal: y(t): mu=1.5');
+xlabel('time'); ylabel('Amplitude');

Assignment/Q4.m

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+%%
+%   Q6. Program to implement ASK, PSK And QAM
+b=randi(0:1,1,10);
+subplot(3,2,1);
+n=length(b);
+t=0:0.01:n;
+x=1:(n+1)*100;
+
+for i=1:n
+  for j=i:.1:i+1
+    a(x(i*100:(i+1)*100))=b(i);
+  end
+end
+a=a(100:end);
+plot(t,a,'r')
+title("Random Generated Bit Pattern"); xlabel("n");ylabel("Bit value");
+%%
+s=a.*sin(2*pi*5*t);
+subplot(3,2,2)
+plot(t,s,'g')
+title("ASK Plot"); xlabel("t");ylabel("Amplitude");
+%%
+%PSK
+for i=1:n
+  if b(i)==0
+    p(i)=-1;
+  else
+    p(i)=1;
+  end
+  for j=i:.1:i+1
+    ps(x(i*100:(i+1)*100))=p(i);
+  end
+end
+ps=ps(100:end);
+s=ps.*sin(2*pi*5*t);
+subplot(3,2,3)
+plot(t,s,'b')
+title("PSK Plot"); xlabel("t");ylabel("Amplitude");
+%%
+%FSK
+for i=1:n
+  if b(i)==0
+    p(i)=-1;
+  else
+    p(i)=1;
+  end
+  for j=i:.1:i+1
+    f(x(i*100:(i+1)*100))=p(i);
+  end
+end
+f=f(100:end);
+s=sin(2*pi*7.5*t+(2*pi*2.5*t).*f);
+subplot(3,2,4)
+plot(t,s,'m')
+title("FSK Plot"); xlabel("t");ylabel("Amplitude");
+%%
+M = 16;
+k = log2(M);
+n2 = 50000;
+nps = 1; % number per sample
+
+rng default
+data = randi([0,1],n2,1);
+subplot(3,2,5);
+stem(data([1:40]));
+title('Random binary bits');
+xlabel('Bit index');
+ylabel('bits value');
+
+four_bit_data = reshape(data , length(data)/k ,k); % creates 4 bit data for QAM
+datanew = bi2de(four_bit_data);                    % converts 4 bit binary data to decimal value
+
+subplot(3,2,6);
+stem(datanew([1:40]));
+title('random value');
+xlabel('index value');
+ylabel('Integer value');
+
+modulated_data = qammod(datanew , M ,'bin');
+Eb = 10;
+snr = Eb + 10*log10((k)/(nps));
+recieved_signal = awgn(modulated_data , snr , 'measured');
+
+newplot = scatterplot(recieved_signal,1,0,'b.');
+hold on;
+scatterplot(modulated_data,1,0,'k+',newplot);
+

Assignment/Q5.m

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+a = -100; b = 100;
+x=-100:100;
+mu = (a + b)/2;
+ 
+
+p1 = @(s)-0.5 * ((x - mu)/s) .^ 2;
+p2 = @(s)(s * sqrt(2*pi));
+f=@(s)exp(p1(s)) ./ p2(s);
+%%
+X = 100.*f(30);  %sigma=30
+subplot(4,2,1)
+plot(x,X,'r')
+grid on
+title('X: Gauss Distribution:Bell Curve')
+xlabel('Randomly produced numbers')
+ylabel('Gauss Distribution')
+%%
+Y = 100.*f(10);
+subplot(4,2,2)
+plot(x,Y,'g')
+grid on
+title('Y: Gauss Distribution:Bell Curve')
+xlabel('Randomly Variables')
+ylabel('Gaussian Distribution')
+%%
+X2=X.^2;
+subplot(4,2,3)
+plot(x,X2,'b')
+grid on
+title('X^2, X: Gaussian')
+xlabel('Randomly Variables')
+ylabel('Gaussian Distribution')
+%%
+Y2=Y.^2;
+subplot(4,2,4)
+plot(x,Y2,'c')
+grid on
+title('Y^2, Y: Gaussian')
+xlabel('Randomly Variables')
+ylabel('Distribution')
+%%
+Z2=X2+Y2;
+subplot(4,2,5)
+plot(x,Z2,'m')
+grid on
+title('X^2+Y^2, X & Y: Gaussian')
+xlabel('Randomly Variables')
+ylabel('Distribution')
+%%
+Z=Z2.^0.5;
+subplot(4,2,6)
+plot(x,Z,'y')
+grid on
+title('Z=(X^2+Y^2)^0^.^5, X: Gaussian')
+xlabel('Randomly Variables')
+ylabel('Distribution')
+%%
+P=exp(X);  %sigma=30
+subplot(4,2,7)
+plot(x,P,'k')
+grid on
+title('P= e^X, X: Gaussaian Distribution')
+xlabel('Randomly Variables')
+ylabel('Distribution')

Assignment/Q6.m

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+%%
+%Nakagami-m Distribution
+clc; clear all; close all;
+colors=['r','g','b'] ;
+m = 1;
+x = [0:0.05:3];
+subplot(411)
+for w = 1:3
+    for ii = 1:length(x)
+        y(ii)=((2*m^m)/(gamma(m)*w^m))*x(ii)^(2*m-1)*exp(-((m/w)*x(ii)^2));
+    end
+    plot(x,y,colors(w))
+    hold on
+end
+xlabel('Support'); 
+ylabel('PDF'); 
+title('Nakagami-m Distribution:Probability Density Function')
+hleg1 = legend('w=1','w=2','w=3');
+set(hleg1,'Location','NorthEast')
+axis([0 3 0 2]);
+grid on 
+%%
+x = (10:1000:125010)';
+y = lognpdf(x,log(20000),1.0);
+
+subplot(412)
+plot(x,y)
+title('Log Normal Distribution')
+h = gca;
+h.XTick = [0 30000 60000 90000 120000];
+h.XTickLabel = {'0','$30,000','$60,000','$90,000','$120,000'};
+% Compute the Lognormal Distribution pdf
+% Suppose the income of a family of four in the United States follows
+% a lognormal distribution with mu = log(20,000) and sigma = 1.
+% Compute and plot the income density
+
+%%
+mu = 1:5;
+
+y = gampdf(1,1,mu);
+%y = [0.3679  0.3033  0.2388  0.1947  0.1637]
+y1 = exppdf(1,mu);
+subplot(413)
+plot(mu,y,mu,y1)
+title("Gamma Distribution Function")
+%%
+%Rician 
+x = linspace(0, 8, 100);
+
+subplot(4, 1, 4)
+plot(x, ricepdf(x, 0, 1),  x, ricepdf(x, 1, 0.50), x, ricepdf(x, 1, 1.00))
+title('Rice PDF with s = 1')
+function y = ricepdf(x, v, s)
+s2 = s.^2; % (neater below)
+    try
+        y = (x ./ s2) .*...
+            exp(-0.5 * (x.^2 + v.^2) ./ s2) .*...
+            besseli(0, x .* v ./ s2);
+            % besseli(0, ...) is the zeroth order modified Bessel function of
+            % the first kind. (see help bessel)
+        y(x <= 0) = 0;
+    catch
+        error('ricepdf:InputSizeMismatch','Non-scalar arguments must match in size.');
+    end
+end
+%%