A unified framework for the Bertrand distribution and the Altes distribution: the new hyperbolic class of quadratic time-frequency distributions

The Bertrand (1991) distribution, which is a member of the affine class of time-frequency distributions (TFDs), and the Altes (1970, 1990) distribution, which does not belong to any known class of TFDs, are studied. It is shown that both TFDs are closely related to a hyperbolic time-frequency geometry. Based on this geometry, a new hyperbolic class of TFDs which contains both the Bertrand distribution and the Altes distribution is defined and studied. It is shown that the hyperbolic class can be derived from the Cohen's (1966) class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.<<ETX>>

[1]  Franz Hlawatsch,et al.  Duality and classification of bilinear time-frequency signal representations , 1991, IEEE Trans. Signal Process..

[2]  Olivier Rioul,et al.  Time-scale energy distributions: a general class extending wavelet transforms , 1992, IEEE Trans. Signal Process..

[3]  F. Hlawatsch,et al.  Quadratic time-frequency distributions: the new hyperbolic class and its intersection with the affine class , 1992, [1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing.

[4]  Richard A. Altes,et al.  Wide-band, proportional-bandwidth Wigner-Ville analysis , 1990, IEEE Trans. Acoust. Speech Signal Process..

[5]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[6]  Franz Hlawatsch,et al.  Regularity and unitarity of bilinear time-frequency signal representations , 1992, IEEE Trans. Inf. Theory.

[7]  L. Cohen.  Generalized Phase-Space Distribution Functions , 1966 .

[8]  T. W. Parks,et al.  Affine Wigner distributions , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  R. Altes,et al.  Bat Signals as Optimally Doppler Tolerant Waveforms , 1970 .