The Top-hat filter is several real-space or Fourier space filtering techniques. The name top-hat originates from the shape of the filter, which is a rectangle function, when viewed in the domain in which the filter is constructed.
Contents |
Real space
In real-space the filter performs nearest-neighbour filtering, incorporating components from neighbouring y-function values. However, despite their ease of implementation their practical use is limited as the real-space representation of a top-hat filter is the
Analogue implementations
Exact non-digital implementations are only theoretically possible. Top-hat filters can be constructed by chaining theoretical low-band and high-band filters. In practice, an approximate top-hat filter can be constructed in analogue hardware using approximate low-band and high-band filters.
Fourier space
In Fourier space, a top hat filter selects a band of signal of desired frequency by the specification of a lower and upper bounding frequencies. Top-hat filters are particularly easy to implement digitally.
Related functions
The top hat function can be generated by differentiating a linear ramp function of width ε. The limit of ε then becomes the delta function. It's real-space form is the same as the moving average, with the exception of not introducing a shift in the output function.
References
 |
This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2008) |
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
