Brickwall filter
In signal processing, a sinc filter is an idealized filter that removes all frequency components above a given cutoff frequency, without affecting lower frequencies, and has linear phase response. The filter's impulse response is a sinc function in the time domain, and its frequency response is a rectangular function.
It is an "ideal" low-pass filter in the frequency sense, perfectly passing low frequencies, perfectly cutting high frequencies; and thus may be considered to be a brick-wall filter.
Real-time filters can only approximate this ideal, since an ideal sinc filter (a.k.a. rectangular filter) is non-causal and 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:
where is an arbitrary cutoff frequency (a.k.a. bandwidth). The impulse response of such a filter is given by the inverse Fourier transform of the frequency response:
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