How can i create a convolution using toeplitz matrix?

Hello ,

i want to create a convolution between two signals but i need to make this happen using the teoplitz command that creates a toeplitz matrix .The problem here is that my first signal (h) is 1x5 matrix and the other signal (a) is 1x21 matrix .The process should be y=toeplitz(h or a) .* transpose(h or a) .How can i create the convolution using the toeplitz command in matlab?

thank you.

Answer 1

[Matt J]

Consider

>> x=1:5, y=rand(1,5),

x =

     1     2     3     4     5


y =

    0.2899    0.4714    0.8782    0.6555    0.3184

and notice,

>> v1=(tril(toeplitz(x))*y(:)).'

v1 =

    0.0306    0.6362    2.2098    4.2551    6.6630

>> v2=conv(x,y); v2=v2(1:numel(v1))

v2 =

    0.0306    0.6362    2.2098    4.2551    6.6630

[Gn Gnk]

Thank you a lot fo your answer . But the main problem still remains because i have a matrix 1x5 and another one 1x21 .In your helpful example you use two 1x5 matrixes .what shoud i do when the one is bigger than the other one ?

[Matt J]

Zero-pad.

[Gn Gnk]

Thank you a lot!