If you call multiplying the Fourier transform by a linear function "high-pass filtering" and dividing by a linear function "low-pass filtering", then I understa

If you call multiplying the Fourier transform by a linear function "high-pass filtering" and dividing by a linear function "low-pass filtering", then I understand what you are saying. But I'm not accustomed to calling those high-pass filters and low-pass filters. I think of high- and low-pass filters as multiplying the Fourier transform by a step function (ideally, or some close approximation of such).