TY - GEN
T1 - Regularity and unitarity of affine and hyperbolic time-frequency representations
AU - Hlawatsch, Franz
AU - Papandreou, Antonia
AU - Boudreaux-Bartels, G. Faye
PY - 1993/1/1
Y1 - 1993/1/1
N2 - The affine and hyperbolic classes of quadratic time-frequency representations (QTFRs) provide frameworks for multiresolution or constant-Q time-frequency analysis. This paper studies the QTFR properties of regularity (QTFR reversibility) and unitarity (preservation of inner products, Moyal's formula) in the context of affine and hyperbolic QTFRs. We 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.
AB - The affine and hyperbolic classes of quadratic time-frequency representations (QTFRs) provide frameworks for multiresolution or constant-Q time-frequency analysis. This paper studies the QTFR properties of regularity (QTFR reversibility) and unitarity (preservation of inner products, Moyal's formula) in the context of affine and hyperbolic QTFRs. We 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.
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M3 - Conference contribution
AN - SCOPUS:0027210168
SN - 0780309464
T3 - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
SP - 111.245-248
BT - Digital Speech Processing
PB - Publ by IEEE
T2 - 1993 IEEE International Conference on Acoustics, Speech and Signal Processing
Y2 - 27 April 1993 through 30 April 1993
ER -