A filter with frequency response $H(f)=\operatorname{sinc}(f).$

Question

In signal processing, a sinc filter is an idealized filter that have the following frequency response $$H(f) = \mathrm{rect} \left( \frac{f}{2B} \right)$$ that is the rectangular function. In the real world, no filter has a frequency response constant (in magnitude) within the band of interest, as well as no filter response has exactly nothing in the exclusion zone of the filter, but my question is another. Is there, in the literature, a filter which has sinc frequency response? Thus: $$H(f)=\operatorname{sinc}(f).$$ Thank you very much.

Answer 1

Yes, there is, e.g. a zero-order hold, which can be modeled as rectangular pulse in the time domain. It's frequency response is a sinc function (possible with a linear phase term accounting for the delay of half the pulse width).

Another example - in discrete-time - would be a moving average filter, where the past $N$ input signal values are averaged. This corresponds to a rectangular impulse response, i.e. $h[n]=1/N$, $n=0,1,\ldots,N-1$. In the frequency domain this is again a sinc function (plus a phase term due to causality).