## Abstract We show that the recently discovered WILSON bases of exponential decay are unconditional bases for all modulation spaces on __R__, including the classical BESSEL potential spaces, the Segal algebra __S__~o~, and the SCHWARTZ space. As a consequence we obtain new bases for spaces of enti
Modulated Malvar–Wilson Bases
✍ Scribed by R.R. Coifman; G. Matviyenko; Y. Meyer
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 111 KB
- Volume
- 4
- Category
- Article
- ISSN
- 1063-5203
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✦ Synopsis
New orthonormal bases of improved time frequency atoms are constructed. These atoms are similar to R. Baraniuk's "chirplets." These new bases are used to unfold frequency modulated signals in the time frequency plane. The selection of the "best basis" amounts to finding an optimal covering with Heisenberg boxes with arbitrary eccentricities and orientations. This analysis is as sharp as the one provided by the Wigner transform.
📜 SIMILAR VOLUMES
In this paper, we construct two-dimensional continuous (smooth) Malvar wavelets defined on a hexagon A, which constitute an orthonormal basis of L 2 (A). The method can be generalized to many hexagons.
## Abstract A sample realizable method for terahertz wave modulation is demonstrated experimentally by using optical controllable ultra‐high resistivity silicon wafer. With modulated 100 mw of 808 nm CW light, a maximum of 21 dB terahertz attenuation was achieved with 0.2 kb/s of modulation speed.
We characterize module bases of spline spaces in terms of their determinants, degree sequences, and dimension series. These characterization also provide tests for freeness of the module. Applications are given to the basis and dimension problem for spline spaces.