\omega.\]`

If `$g(t)$` is smooth,  the convolution creates a *smoothed version* of `$f(t)$`.

If `$g(t)$` has a Fourier transform `$G(\omega)$` is localized in the vicinity of a certain frequency `$\omega_o$`, then  `$h(t)$` will also be localized around `$\omega_o$`.

In this case the convolution becomes a *bandpass filter*.


--
What is a good example of a function `$g(t)$` whose Fourier transform `$G(\omega)$` is localized around zero?


--
What is a good example of a function `$g(t)$` whose Fourier tra