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dc.contributor.authorBaraniuk, Richard G.
Jones, Douglas L.
dc.creatorBaraniuk, Richard G.
Jones, Douglas L. 2007-10-31T00:34:53Z 2007-10-31T00:34:53Z 1993-12-01 2004-01-09
dc.identifier.citation R. G. Baraniuk and D. L. Jones, "Shear Madness: New Orthonormal Bases and Frames Using Chirp Functions," IEEE Transactions on Signal Processing, vol. 41, no. 12, 1993.
dc.description Journal Paper
dc.description.abstract The proportional-bandwidth and constant-bandwidth time-frequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular tessellations of the time-frequency plane. While much effort has gone into methods for designing nice wavelet and window functions for these frameworks, little consideration has been given to methods for constructing orthonormal bases employing nonrectangular time-frequency tilings. In this correspondence, we take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear, or chirp, in the time­frequency plane, in addition to translate and scale. The new scale­-shear fan bases and shift­-shear chevron bases are obtained by operating on an existing wavelet, Gabor, or Wilson basis set with two special unitary warping transformations. In addition to the theoretical benefit of broadening the class of valid time­frequency plane tilings, these new bases could possibly also be useful for representing certain types of signals, such as chirping and dispersed signals.
dc.language.iso eng
dc.subjectnonstationary signals
valid time-frequency plane tilings
dc.subject.otherTime Frequency and Spectral Analysis
dc.title Shear Madness: New Orthonormal Bases and Frames Using Chirp Functions
dc.type Journal article
dc.citation.bibtexName article
dc.citation.journalTitle IEEE Transactions on Signal Processing 2006-07-24
dc.contributor.orgDigital Signal Processing (
dc.subject.keywordnonstationary signals
valid time-frequency plane tilings
dc.citation.volumeNumber 41
dc.citation.issueNumber 12
dc.type.dcmi Text
dc.type.dcmi Text
dc.citation.firstpage 3543
dc.citation.lastpage 3549

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