Regularity and unitarity of affine and hyperbolic time-frequency representations

The affine and hyperbolic classes of quadratic time-frequency representations (QTFRs) provide frameworks for multiresolution or constant-Q time-frequency analysis. The authors study the QTFR properties of regularity (QTFR reversibility) and unitarity (preservation of inner products, Moyal's formula) in the context of affine and hyperbolic QTFRs. They develop the calculus of inverse kernels and discuss important implications of regularity and unitarity, such as signal recovery, the derivation of other quadratic signal representations, optimum detection, least-squares signal synthesis, the effect of linear signal transforms, and the construction of QTFR basis systems.<>