Wave-shape function analysis. When cepstrum meets time-frequency analysis. (English) Zbl 1394.42029
A signal with time-varying, approximately periodic behavior is modeled as
\[
f(t) = A(t) s(\phi(t)).
\]
Here \(A(t)\) is the amplitude function, \(s(t)\) the wave shape function (periodic, but not necessarily sinusoidal), and \(\phi(t)\) is the phase function. \(\phi'(t)\) represents the instantaneous frequency. Examples of such signals include human respiration or ECG signals.
The goal of the algorithm proposed in this paper is to do a time-frequency analysis that estimates amplitude and phase in a small interval, independent of the wave shape.
The \(\gamma\)-generalized cepstrum or root cepstrum of a signal \(f(t)\) is defined as the inverse Fourier transform of the \(\gamma\)-power of the Fourier transform of \(f\): \[ \tilde f_\gamma(q) = \int \left| \hat f(\xi) \right|^\gamma e^{2\pi i q \xi} \,d\xi. \] By replacing the Fourier transform with the short-time Fourier transform, you can define a short-time cepstral transform. This forms the basis of the proposed algorithm DSST (de-shape synchro-squeezing transform).
The algorithm is analyzed, and illustrated with several examples, both synthetic data and measured signals.
The goal of the algorithm proposed in this paper is to do a time-frequency analysis that estimates amplitude and phase in a small interval, independent of the wave shape.
The \(\gamma\)-generalized cepstrum or root cepstrum of a signal \(f(t)\) is defined as the inverse Fourier transform of the \(\gamma\)-power of the Fourier transform of \(f\): \[ \tilde f_\gamma(q) = \int \left| \hat f(\xi) \right|^\gamma e^{2\pi i q \xi} \,d\xi. \] By replacing the Fourier transform with the short-time Fourier transform, you can define a short-time cepstral transform. This forms the basis of the proposed algorithm DSST (de-shape synchro-squeezing transform).
The algorithm is analyzed, and illustrated with several examples, both synthetic data and measured signals.
Reviewer: Fritz Keinert (Ames)
MSC:
| 42C20 | Other transformations of harmonic type |
| 62-07 | Data analysis (statistics) (MSC2010) |
Keywords:
adaptive non-harmonic model; cepstrum; short-time cepstral transform; synchrosqueezing transform; de-shape STFT; de-shape SSTReferences:
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