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Supratik Das on 23 Sep 2021
Commented: Supratik Das on 23 Sep 2021
clc, clear all, close all
d=sin(0.05*pi*(1:200)+2*pi*rand);
g=randn(1,200);
v1=filter(1,[1 -0.8],g);
v2=filter(1,[1 0.6],g);
x=d+v1;
figure(1)
plot(1:100,x(1:100),'b','linewidth',1.2)
hold on
plot(1:100,d(1:100),'r','linewidth',1.2)
grid on
xlabel('n')
legend('x(n)','d(n)')
title('plot of x(n) and d(n)')
figure(2)
plot(1:100,v2(1:100),'b','linewidth',1.2)
grid on
xlabel('n')
title('plot of v_2(n)')
Rv2=covar(v2,4);
figure(3)
stem(Rv2,'b','linewidth',1.2)
grid on
xlabel('k')
title('autocorrelation of v_2(n)')
rxv2=convm(x,4)'*convm(v2,4)/(length(x)-1);
figure(4)
stem(rxv2,'b','linewidth',1.2)
grid on
xlabel('k')
title('cross-correlation between x(n) and v_2(n)')
w=rxv2(1,:)/Rv2;
v1hat=filter(w,1,v2);
dhat=x-v1hat;
figure(5)
plot(dhat(1:100))
hold on
plot(d(1:100),'r')
xlabel('n')
title('Estimated d(n) vs actual d(n)')
legend('Estimate d(n)', 'Actual d(n)')
##### 2 CommentsShowHide 1 older comment
Supratik Das on 23 Sep 2021

Walter Roberson on 23 Sep 2021
clc, clear all, close all
d=sin(0.05*pi*(1:200)+2*pi*rand);
g=randn(1,200);
v1=filter(1,[1 -0.8],g);
v2=filter(1,[1 0.6],g);
x=d+v1;
figure(1)
plot(1:100,x(1:100),'b','linewidth',1.2)
hold on
plot(1:100,d(1:100),'r','linewidth',1.2)
grid on
xlabel('n')
legend('x(n)','d(n)')
title('plot of x(n) and d(n)')
figure(2)
plot(1:100,v2(1:100),'b','linewidth',1.2)
grid on
xlabel('n')
title('plot of v_2(n)')
Rv2=covar(v2,4);
ans = 1×2
204 5
size(Rv2)
ans = 1×2
5 5
figure(3)
stem(Rv2,'b','linewidth',1.2)
grid on
xlabel('k')
title('autocorrelation of v_2(n)')
cmx = convm(x,4);
cmv2 = convm(v2,4);
rxv2 = cmx'*cmv2/(length(x)-1);
size(cmx), size(cmv2), size(rxv2)
ans = 1×2
203 4
ans = 1×2
203 4
ans = 1×2
4 4
figure(4)
stem(rxv2,'b','linewidth',1.2)
grid on
xlabel('k')
title('cross-correlation between x(n) and v_2(n)')
size(rxv2), size(Rv2)
ans = 1×2
4 4
ans = 1×2
5 5
w=rxv2(1,:)/Rv2;
Error using /
Matrix dimensions must agree.
v1hat=filter(w,1,v2);
dhat=x-v1hat;
figure(5)
plot(dhat(1:100))
hold on
plot(d(1:100),'r')
xlabel('n')
title('Estimated d(n) vs actual d(n)')
legend('Estimate d(n)', 'Actual d(n)')
function R = covar(x,p)
%
% This function sets up a covariance matrix
%
x = x(:);
m = length(x);
x = x - ones(m,1)*(sum(x)/m);
cm = convm(x,p+1);
size(cm)
R = cm'*cm/(m-1);
end
function X = convm(x,p)
%
% This function sets up a convolution matrix
%
N = length(x)+2*p-2;
x = x(:);
for i=1:p
end
end
What is happening is that you are creating one of your variables by calling covar(), which adds 1 to the second parameter (4) to get the size -- so it will be something by 5. But the other variable you get by calling convm(), which does not add 1 to the second parameter (4), so it will be something by 4. The 5 and 4 then become incompatible sizes.
Supratik Das on 23 Sep 2021
so how to solve this problem?

Shayan Sepahvand on 23 Sep 2021
Hi,
the first argument of
covar(sys, w)
should be some LTI system (discrete in your case), I suggest you to first derive the LTI form of v2 using z transform, then use covar
good luck
Supratik Das on 23 Sep 2021