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Transformation, inversion and conversion of bilinear signal representations

Bilinear signal parameters and representations can be described in terms of linear operators. Such a description yields a deeper understanding and a systematic calculus of bilinear time-frequency signal representations such as Wigner distribution, ambiguity function and spectrogram. Basic points of time-frequency representations, like transformations, properties and constraints, inversion and conversion, are discussed in a formal way. The inversion problem leads to the definition of regular representations, where the regularity property makes sure that no essential information about signals is lost.