Time-frequency signal analysis: issues and alternative methods

The classical technique for characterizing the time evolution behavior of nonstationary signals is the short-time Fourier transform (STFT), a linear time-frequency representation (TFR) analysis technique. Beginning with the Wigner-Ville function (WVF), a plethora of quadratic TFR techniques have been introduced in an attempt to improve the time-vs.-frequency resolving detail over that achievable with the STFT. This paper makes the case that this improvement, in practice, is approximately a factor of only two and cannot be achieved without the introduction of non-negligible cross-term artifacts and the sacrifice of detectable dynamic range. Two alternative TFR techniques are defined and demonstrated with capabilities to achieve the factor of two detail improvement without the cross-term artifacts and dynamic range degradation inherent with quadratic TFR techniques. One alternative, based on a variant of two-dimensional (2-D) minimum variance spectral analysis, exploits two new 2-D functions: the windowed data function (WDF) and the transformed WDF function (TWF). The other alternative is based on subspace-enhanced linear predictive extrapolation. An additional contribution of this paper is an analysis procedure for handling persistent nonstationary signals, in contrast to most TFR methods found in the literature that deal with short-duration (transient) nonstationary signal events.