Chirplet transform
Image:Wave-chirp-wavelet-chirplet-en.svg|thumb|244px|Comparison of wave, wavelet, chirp, and chirplet
Image: Pete with deltyburn abakography robot chirplet c.jpg|thumb|244px|Chirplet in a computer-mediated reality environment.
In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.
Similar to the wavelet transform, chirplets are usually generated from a single mother chirplet.
Definitions
The term chirplet transform was coined by Steve Mann, as the title of the first published paper on chirplets. The term chirplet itself was also used by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words:The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time–frequency plane. Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the chirplet transform described specific signal representations based on families of functions related to one another by time–varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes. In that paper, the Gaussian chirplet transform was presented as one such example, together with a successful application to ice fragment detection in radar. The term chirplet was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell later that same year.
Applications
[Image:P-type-chirplets-for-image-processing.png|thumb|245px|(a) In image processing, periodicity is often subject to projective geometry (i.e. chirping that arises from projection). (b) In this image, repeating structures like the alternating dark space inside the windows, and light space of the white concrete, chirp (increase in frequency) towards the right. (c) The chirplet transform is able to represent this modulated variation compactly.]The first practical application of the chirplet transform was in water-human-computer interaction for marine safety, to assist vessels in navigating through ice-infested waters, using marine radar to detect growlers.
Other applications of the chirplet transform in WaterHCI include the SWIM.
More recently other practical applications have been developed, including image processing,
as well as to excise chirp-like interference in spread spectrum communications, in EEG processing, and Chirplet Time Domain Reflectometry.