Sinc filter

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In signal processing, a sinc filter is an idealized filter that removes all frequency components above a given bandwidth and leaves the low frequencies alone. It is shaped like a rectangular function in the frequency domain and like a sinc function in the time domain. Realistic filters can only approximate this, since an ideal sinc filter (aka rectangular filter) has an infinite delay, but it is commonly found in conceptual demonstrations or proofs, such as the sampling theorem and the Whittaker–Shannon interpolation formula.

In mathematical terms, the desired frequency response is the rectangular function:

$H(f) = \mathrm{rect} \left( \frac{f}{2B} \right)$

where $B\,$ is an arbitrary cutoff frequency (aka bandwidth) (in Hz). The impulse response of such a filter is given by the inverse Fourier transform:

$h(t) = \mathcal{F}^{-1} \{ H \}(t)$	$= 2B\cdot \frac{\sin(2\pi Bt)}{2\pi Bt}$
	$= 2B\cdot \mathrm{sinc}(2B\cdot t)\,$ , in terms of the normalized sinc function.