A convolution of a convolution

[thrillhouse86]

Hi,
can someone please give me an example of what a convolution of a convolution would look like ?

Thanks

 

[Char. Limit]

What do you mean by "look like"?

 

[thrillhouse86]

as in:
$$f*g = \int^{\infty}_{-\infty} f(\tau)g(t-\tau) d\tau$$

what would
h*(f*g) look like ?

-Thrillhouse

 

[pbandjay]

I should think something along these lines:

$$(f*g)(t) \stackrel{\mathrm{def}}{=} \displaystyle\int_{-\infty}^\infty f(x)g(t - x) dx$$

$$(h*(f*g))(t) = \displaystyle\int_{-\infty}^\infty h(y)(f*g)(t - y) dy = \displaystyle\int_{-\infty}^\infty h(y) \left( \displaystyle\int_{-\infty}^\infty f(x)g(t - y - x) dx \right) dy$$

 

[thrillhouse86]

thanks pbandjay