Title :
On collections of joint time-frequency functions generated by biorthogonal-like functions
Author :
Lu, Youhong ; Morris, Joel M.
Author_Institution :
Dept. of Electr. Eng., Maryland Univ., Baltimore, MD, USA
Abstract :
We generalize the Gabor (1946) expansion via a biorthogonal-like function theory. We show that a pair of biorthogonal-like functions (BLFs) form a pair of analysis and synthesis functions for the Gabor expansion. Moreover, the pair of collections used in the Gabor expansion must be generated by a pair of BLFs; BLF theory, therefore, covers frame theory and basis theory for the Gabor expansion. Two efficient computation methods for BLFs and examples are presented. It is shown that the signal representation in the joint time-frequency domain is completely determined by the existence of BLFs and solutions to the biorthogonal-like condition
Keywords :
functional analysis; signal representation; time-frequency analysis; Gabor expansion; analysis functions; basis theory; biorthogonal-like condition; biorthogonal-like function theory; biorthogonal-like functions; computation methods; frame theory; joint time-frequency functions; signal representation; synthesis functions; Biomedical signal processing; Hilbert space; Laboratories; Sampling methods; Signal generators; Signal synthesis; Time frequency analysis;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1994., Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Philadelphia, PA
Print_ISBN :
0-7803-2127-8
DOI :
10.1109/TFSA.1994.467331
