A measurement method based on an improved version of the chirplet transform for instantaneous frequency estimation

A measurement method for instantaneous frequency estimation is presented in the paper. The method is based on the use of the chirplet transform, a linear time-frequency representation (TFR) allowing additional modifications of each cell on the time-frequency plane with respect to other TFRs. In particular, a modified version of this transform is here proposed; a bending effect can further be imposed on the cells. Thanks both to this feature and a suitable measurement procedure, properly set up by the authors, the method grants both a satisfactory accuracy in reconstructing the instantaneous frequency trajectory of monocomponent signals and an good resolving capability in the analysis of multicomponent signals whose instantaneous frequency trajectories are strongly nonlinear and very close to one another. Details concerning the theory underlying the chirplet transform and the proposed modified version are first given. Then, the measurement procedure for optimizing the values of the parameters of the transform according to the local features of the analyzed signal is described in detail. Finally, the results of several experimental tests conducted both on monocomponent and multicomponent signals are presented; advantages over other solutions are also highlighted.

[1]  Kon Max Wong,et al.  Estimation of the time-varying frequency of a signal: the Cramer-Rao bound and the application of Wigner distribution , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  Richard G. Baraniuk,et al.  Instantaneous Frequency Estimation Using the Reassignment Method , 1997 .

[3]  P. Flandrin,et al.  INSTANTANEOUS FREQUENCY ESTIMATION : BAYESIAN APPROACHES versus REASSIGNMENT -- APPLICATION TO GRAVI - Acoustics, Speech, and Signal Processing, 1996. ICASSP-96. Conference Proceedings., 1996 IEEE Inte , 2004 .

[4]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[5]  Douglas L. Jones,et al.  Unitary equivalence: a new twist on signal processing , 1995, IEEE Trans. Signal Process..

[6]  S. Barbarossa,et al.  Analysis of nonlinear FM signals by pattern recognition of their time-frequency representation , 1996, IEEE Signal Processing Letters.

[7]  Braham Barkat,et al.  Instantaneous frequency estimation of polynomial FM signals using the peak of the PWVD: statistical performance in the presence of additive gaussian noise , 1999, IEEE Trans. Signal Process..

[8]  Douglas L. Jones,et al.  Wigner-based formulation of the chirplet transform , 1996, IEEE Trans. Signal Process..

[9]  Gregorio Andria,et al.  Interpolated smoothed pseudo Wigner-Ville distribution for accurate spectrum analysis , 1996 .

[10]  Pasquale Daponte,et al.  The detection of echoes from multilayer structures using the wavelet transform , 2000, IEEE Trans. Instrum. Meas..

[11]  P. Flandrin,et al.  Chirp hunting , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[12]  S. Haykin,et al.  Time-frequency perspectives: the 'chirplet' transform , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  Aykut Bultan.  A four-parameter atomic decomposition of chirplets , 1999, IEEE Trans. Signal Process..

[14]  Guy Drijkoningen,et al.  Time-frequency analysis of seismic reflection signals , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[15]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[16]  Pasquale Daponte,et al.  A measurement method based on the wavelet transform for power quality analysis , 1998 .

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

[18]  O. Arikan,et al.  A parallelized matching pursuit algorithm for the four-parameter chirplet decomposition , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[19]  Srdjan Stankovic,et al.  An analysis of instantaneous frequency representation using time-frequency distributions-generalized Wigner distribution , 1995, IEEE Trans. Signal Process..

[20]  Simon Haykin,et al.  The chirplet transform: physical considerations , 1995, IEEE Trans. Signal Process..