Convolution Computations results for a system response.

Can anyone tell the difference of these plots that I used following two codes to plot the results of convolution computations given and need to know the reason for having following difference?

I have attached the results I got for these codes.

Answer 1

[Bruno Luong]

You make few mistakes, indexing and flipping (see careful conv documentation, the subtility is there, though TMW never mention whereas CEIL or FLOOR must be applied on even-length kernel, shame on them).

This code will show the correction and match both calculations (roundoff beside)

n=[1:1:1000]; 
s=10*cos(0.05*n);
N=randn(1,1000);
x=s+N;
h=0.1*ones(1,10);

y = conv(x,h,'same'); % 'same'

yy = zeros(1,length(n));
for i = 1: length(n)
    for j = 1:length(h)
        k =  i-j+ceil((length(h)+1)/2); % shift by ceil(...) which correspond to "same"
        if k>=1 && k<=length(x) % overflow check
            yy(i) = yy(i) + h(j)*x(k);
        end
    end
end

close all
figure
plot(yy)
hold on
plot(y)

Related post here

[Prasad Edirisuriya Mudiyanselage]

Thank you!