Given that the convolution definition as far as I am aware is:
$(f*g)(t) = \int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau$
Here I see that the functions f
and g
are being shifted across the time domain. I wonder if there is an equivalent for the scaling the time domain such at:
$(f?g)(t) = \int_{-\infty}^\infty f(\tau)g(t\tau)d\tau$
In my mind this would be similar to how a Fourier transform works (e.g. $g(t\tau)$ would be $cis(t\tau)$. I am not sure what kind of applications this could have in non-periodic data but I am still curious nontheless if there is a proper term for it.