TY - GEN
T1 - New signal-space orthonormal bases via the metaplectic transform
AU - Baraniuk, R. G.
AU - Jones, D. L.
N1 - Funding Information:
‘This work was supported by the Sound Group of the Computer-Based Education Research Laboratory at the Univer- sity of Illinois, the Joint Services Electronics Program,G rant No. N00014-90-J-1270a,n d the National Science Foundation, Grant No. MIP 90-12747. R. Baraniuk is an leave from Rice University, P.O.B ox 1892, Houston, Texas 77251-1892, USA.
Publisher Copyright:
© 1992 IEEE.
PY - 1992
Y1 - 1992
N2 - 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.
AB - 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.
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U2 - 10.1109/TFTSA.1992.274169
DO - 10.1109/TFTSA.1992.274169
M3 - Conference contribution
AN - SCOPUS:33747841549
T3 - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
SP - 339
EP - 342
BT - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
Y2 - 4 October 1992 through 6 October 1992
ER -