## Regularity and unitarity of bilinear time-frequency signal representations (1992)

Venue: | IEEE Trans. Inform. Theory |

Citations: | 11 - 2 self |

### BibTeX

@ARTICLE{Hlawatsch92regularityand,

author = {Franz Hlawatsch},

title = {Regularity and unitarity of bilinear time-frequency signal representations},

journal = {IEEE Trans. Inform. Theory},

year = {1992},

volume = {38},

pages = {82--94}

}

### OpenURL

### Abstract

Abstract-Two structural properties of bilinear timefrequency representations (BTFR’s) of signals are introduced and studied. The definition of these properties is based on a linear-operator description of BTFR’s. The first property, termed regularity, has important implications with respect to the recovery of signals from their BTFR outcome, the derivation of other bilinear signal representations from a BTFR, the BTFR’s reaction to linear signal transformations, and the construction of bases of induced BTFR-domain spaces. The second property, called uniturity, is equivalent to validity of Moyal’s formula. Unitarity is thus necessary and sufficient for a closed-form solution of optimal signal synthesis and for a BTFR formulation of optimal detection/estimation methods. Besides, unitarity also allows the systematic construction of BTFR “product relations’’ like Wigner distribution’s interference formula and ambiguity