When convolved with an input signal, the sinc filter results in an output signal in which the frequencies up to the cutoff frequency are all included, and the higher frequencies are all blocked. The sinc filter is a scaled version of this that I’ll define below. The sinc function ( normalized, hence the \(\pi\)’s, as is customary in signal processing), is defined as
Theoretically, the ideal (i.e., perfect) low-pass filter is the sinc filter. How to create a simple low-pass filter? A low-pass filter is meant to allow low frequencies to pass, but to stop high frequencies. This article is complemented by a Filter Design tool that allows you to create your own custom versions of the example filter that is shown below, and download the resulting filter coefficients. Summary: This article shows how to create a simple low-pass filter, starting from a cutoff frequency \(f_c\) and a transition bandwidth \(b\).
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