Abstract
The two primary classes of time-frequency-concentrated orthonormal bases (ONBs) can be interpreted a8 arising from the discretization of either the short-time Fourier tranaform (STFT) or the continuous wavelet transform (CWT). Recently, the five-dimensional metaplectic transform (MT) has been proposed as a generalization of the STFT and CWT. It allows shears and rotations of the analyzing window/ wavelet in the time-frequency plane, in addition to translations and scaling. Just as the CWT and STFT can be discretized on lattices of points in two dimensions, the MT can be discretized on lattices of points in five dimensions. In this paper, we consider the discretization of the MT, and show that it can lead to entirely new ONBs for the signal space of square integrable functions. Two new classes of bases, the scale and shear bases and the translation and shear bases, are derived to demonstrate the discretization process. Besides generalizing the current methods of generating time-frequency-concentrated ONBs, MT bases possess extra degrees of freedom that can be used to match a wider variety of signals.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 339-342 |
| Number of pages | 4 |
| ISBN (Electronic) | 0780308050, 9780780308053 |
| DOIs | |
| State | Published - Jan 1 1992 |
| Event | 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Victoria, Canada Duration: Oct 4 1992 → Oct 6 1992 |
Other
| Other | 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |
|---|---|
| Country | Canada |
| City | Victoria |
| Period | 10/4/92 → 10/6/92 |
ASJC Scopus subject areas
- Signal Processing