On the cross-biorthogonal representation
نویسندگان
چکیده
A novel cross term deleted Wigner representation can be obtained by expanding the Wigner Distribution (WD) in terms of two complementary Gabor coe cients of the signal and a translated set of Wigner basis functions. Two such complementary Gabor coe cients of a signal can be obtained by reversing the role of Gabor synthesis window h(t) and its biorthogonal function b(t). Such a representation is de ned here, as 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 tradeo s, (iii) noise reduction and (iv) basis set properties of the XBIO representation are also discussed. Simulation results are provided to substantiate the theoretical ndings.
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