PLEASE HELP!!!! I\'LL GIVE ALL MY POINTS(8250) TO YOU IF YOU GIVE ME CORRECT ANS

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PLEASE HELP!!!! I'LL GIVE ALL MY POINTS(8250) TO YOU IF YOU GIVE ME CORRECT ANSWER...

WRITE A MATLAB CODE FOR FOLLOWING...

B. BY THE YULE-WALKER AR MODEL

MATLAB CODE...

Power Spectrum Estimation Generation of the random sequence x(n) of a known PSD: Generate a white Gaussian random sequence rw(n) of zero mean and variance sigma Pass the sequence through a digital filter to create an output sequence x(n). Now, the PSD of the sequence x(n) is to be estimated from a finite length of the sequence x(n) (say, N = 128).

Explanation / Answer

A. THE WELCH NONPARAMETRIC METHOD:

clear all;

clc;

N=128;

L=8;

F=100;

variance=input('enter the variance');

D=input('enter value D');

WGN= sqrt(variance)*randn(N,1);

figure

plot(WGN);

title('White Gaussian Random Sequence (variiance=1, N=128)');

ylabel('r(n)');

xlabel('n');

num= [1];

den= [1 -0.9 0.81 -0.729];

H1= filt(num,den);

x= filter(num,den,WGN);

figure

plot(x);

title('Filtered Output Sequence');

ylabel('x(n)');

xlabel('n');

M= (N+D*(L-1))/L;

a=zeros(L,M);

for i=1:L

for j=1:M

a(i,j)=x((M-D)*(i-1)+j);

end

end

for n=1:M

w(n)=0.54-0.46*cos((2*pi*(n-1))/(M-1));

end

figure

plot(w);

title('Hamming Window');

ylabel('w(n)');

xlabel('n');

U=0;

for n=1:M

U=U+((w(n))^2)/M;

end

for i=1:L

p(i,:)=zeros(1,F);

f=-0.5:1/(F-1):0.5;

for j=1:M

p(i,:)=p(i,:)+a(i,j)*w(j)*exp(-1i*2*pi*f*(j-1));

end

for k=1:F

P(i,k)=((abs(p(i,k)))^2)/(M*U);

end

end

for k=1:F

Px(k)=0;

for i=1:L

Px(k)=Px(k)+(P(i,k))/L;

end

end

f=-0.5:1/(F-1):0.5;

figure

plot(f,Px);

title('Power Spectrum Density (No Overlapping: D=0)');

ylabel('PSD');

xlabel('frequency');

B. THE YULE-WALKER AR MODEL :

clear all;

clc;

N=128;

F=100;

variance=input('enter the variance ');

p=input('enter value of p ');

WGN= sqrt(variance)*randn(N,1);

figure

plot(WGN);

title('White Gaussian Random Sequence (variiance=1, N=128)');

ylabel('r(n)');

xlabel('n');

num1= [1];

den1= [1 -0.9 0.81 -0.729];

H1= filt(num1,den1);

x= filter(num1,den1,WGN);

figure

plot(x);

title('Filtered Output Sequence');

ylabel('x(n)');

xlabel('n');

for m=1:p+1

r(m)=0;

for n=1:N-m+1

r(m)=r(m)+(x(n)*x(n+m-1))/N;

end

end

for i=1:p

for j=1:p

R(i,j)=r(abs(i-j)+1);

end

end

R1=inv(R);

for i=1:p

R2(i,1)=-r(i+1);

end

a=R1*R2;

temp=0;

for i=1:p

temp=temp+a(i,1)*r(1,i+1);

end

var=r(1)+temp;

num2=[1];

den2=[1 transpose(a)];

H2= filt(num2,den2);

den3=zeros(1,F);

f=-0.5:1/(F-1):0.5;

for j=1:p

den3(1,:)=den3(1,:)+a(j)*exp(-1i*2*pi*j*f);

end

for i=1:F

P(i)=var/((abs(1+den3(1,i)))^2);

end

f=-0.5:1/(F-1):0.5;

figure

plot(f,P);

title('Power Spectrum Density (P=5)');

ylabel('PSD');

xlabel('frequency');

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