# Convolution of $f(2x)$ and $g(3x)$

As I know, convolution is defined as $f(x)*g(x) = \int_{-\infty}^{+\infty}f(\tau)g(x-\tau)d_{\tau}$, but what if we want to convolve $f(2x)$ and $g(3x)$? It should be like $f(2x)*g(3x) = \int_{-\infty}^{+\infty}f(2\tau)g(3x-\tau)d_{\tau}$ or $f(2x)*g(3x) = \int_{-\infty}^{+\infty}f(2\tau)g(3x-3\tau)d_{\tau}$ or anything else?

## 1 Answer

Replace $x$ by $x - \tau$ . So option b i.e $3x-3\tau$.