Spectral estimation-What is new? What is next?

Jean Baptiste Tary, Roberto Henry Herrera, Jiajun Han, Mirko van der Baan
2014 Reviews of Geophysics  
Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization)
more » ... ue to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed. Methods Short-Time Fourier Transform The Fourier transform is a measure of the similarity of a signal with a family basis formed by sines and cosines. This can be expressed as the inner product of a signal s(t) with a template (t), i.e., ⟨s(t), (t)⟩ = ∫ ∞ −∞ s(t) * (t)dt, where * stands for the complex conjugate [Gao et al., 2010] . When this template is made of TARY ET AL.
doi:10.1002/2014rg000461 fatcat:6sm3l7wwbjb47au37oonf4sxim