Title :
On the cross-biorthogonal representation
Author :
Kadambe, Shubha ; Orr, Richard S.
Author_Institution :
Atlantic Aerosp. Electron. Corp., Greenbelt, MD, USA
Abstract :
A novel cross term deleted Wigner representation can be obtained by expanding the Wigner distribution (WD) in terms of two complementary Gabor coefficients of the signal and a translated set of Wigner basis functions. Two such complementary Gabor coefficients of a signal can be obtained by reversing the role of the Gabor synthesis window h(t) and its biorthogonal function b(t). Such a representation is defined here, as the cross-biorthogonal representation (XBIO). Details of derivation of this new representation is provided in this paper. The choice of the synthesis functions and their corresponding biorthogonal functions with respect to (i) concentration/resolution capabilities, (ii) redundancy vs. minimum-dimension tradeoffs, (iii) noise reduction and (iv) basis set properties of the XBIO representation are also discussed. Simulation results are provided to substantiate the theoretical findings
Keywords :
Wigner distribution; interference suppression; noise; signal representation; signal resolution; signal synthesis; Gabor coefficient; Gabor synthesis window; Wigner basis functions; Wigner distribution; XBIO representation; biorthogonal function; concentration; cross term deleted Wigner representation; cross-biorthogonal representation; minimum-dimension tradeoff; noise reduction; redundancy; resolution; synthesis function; Aerospace electronics; Biomedical signal processing; Data mining; Equations; Gabor filters; Noise reduction; Signal processing; Signal resolution; Signal synthesis; Time frequency analysis;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on
Conference_Location :
Munich
Print_ISBN :
0-8186-7919-0
DOI :
10.1109/ICASSP.1997.604653
