Top-hat filter

Despite its ease of implementation, its practical use is limited as the real-space representation of a top-hat filter is the sinc function, which has the often undesirable effect of incorporating non-local frequencies.

In practice, an approximate top-hat filter can be constructed in analogue hardware using approximate low-band and high-band filters.

In Fourier space, a top hat filter selects a band of signal of desired frequency by the specification of lower and upper bounding frequencies.

Top-hat filters are particularly easy to implement digitally.

Its real-space form is the same as the moving average, with the exception of not introducing a shift in the output function.