IEEE Signal Processing - March 2018 - 142
SubSurface exploration:
recent advanceS in Geo-SiGnal proceSSinG,
interpretation, and learninG
Marcus C.B. Andrade,
Milton J. Porsani, and Bjorn Ursin
Complex Autoregressive Time-Frequency Analysis
Estimation of time-varying periodic signal components
T
ime-frequency representations of nonstationary signals
have a wide range of geophysical applications, including
seismics, seismology, volcanology, and astrophysics. In this
article, we estimate a complex autoregressive (AR) model from a
short time window of the analytic signal. The local power spectrum is the inverse of the spectrum of this AR model. Since the
coefficients are complex, the time window can be shorter than
for the real AR model, which requires more coefficients. This
results in higher time-frequency resolution, as seen in a synthetic data examples with different signal components. The new
technique also gives good results when computing the instantaneous average frequency (IAF) of marine seismic data. Applied
to digitized and downloaded data from the Laser Interferometer
Gravitational-Wave Observatory (LIGO) in Hanford, Washington, the result clearly shows the linear chirp associated with the
merger of two black holes.
Introduction
©istockphoto.com/khadi Ganiev
Digital Object Identifier 10.1109/MSP.2017.2783942
Date of publication: 7 March 2018
142
The continuous push for better time-frequency representations
of nonstationary signals over the past decades has produced
many distinct approaches. Overviews of different methods can
be found in [1]-[5]. The classical approach is the spectrogram
[6] or the short-term Fourier transform (STFT) [7], which is
still commonly used. It is a nonparametric method, which
gives all frequency components of a local signal by Fourier
transform of a short time section of the data. It is limited by
the tradeoff between time and frequency resolution (the uncertainty principle, [6]) and spectral leakage.
Many methods are used to estimate the individual components of the signal; see the reviews by [4], [8], and [9]. These
methods include the continuous wavelet transform [10], the
empirical wavelet transform [11], the S-transform [12], the
synchrosqueezing transform [13]-[15], and matching pursuit
[16]. In empirical mode decomposition (EMD) and its extensions [17], [18], the signal is represented by a sum of intrinsic
modes. Variational mode decomposition (VMD) [19] also uses
the analytic signal to decompose a real signal into narrowband components with slowly varying amplitudes. The center
IEEE SIgnal ProcESSIng MagazInE
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March 2018
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Table of Contents for the Digital Edition of IEEE Signal Processing - March 2018
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