Related Work
The chirplet transform is a generalized representation that includes as special cases:
- The Fourier transform
- The short-time Fourier transform (STFT), also known as the spectrogram
- The Wigner-Ville distribution
- The wavelet transform
- Canonical conjugate variables
- Segal–Shale–Weil distribution
Josef Segman proposed the idea of incorporating scale into the Heisenberg group (position, momentum, phase, or equivalently any canonical conjugate variables taken together with phase, such as, for example, time, frequency, and phase). This gave rise to a four parameter space of time, frequency, phase, and scale. Segman introduced this idea of phase scale. (Personal communication with Mann, from Josef Segman, at Harvard University and at Massachusetts Institute of Technology). Further personal communication between Irving Segal (the principal behind the Segal, Shale Weil representation, known also as the metaplectic representation—a double covering of the symplectic group) and Mann led to additional insight into the chirplet transform, in particular, to the variation of the chirplet transform that is based on q-chirplets.
Read more about this topic: Chirplet Transform
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