The effect of mismatching analysis signals and time-frequency representations

We study the time-frequency geometry underlying quadratic time-frequency representations (QTFRs) defined based on a generalized time-shift covariance property. These QTFRs include the generalized warped Wigner distribution (WD) and its smoothed versions that are useful for reducing cross terms in multicomponent signal analysis applications. The generalized warped WD is ideal for analyzing nonstationary signals whose group delay matches the specified time-shift covariance. Its smoothed versions may also be well suited for various signals provided that their smoothing characteristics match the signal's time-frequency structure. Thus, we examine the effects of a mismatch between the analysis signal and the chosen QTFR. We provide examples to demonstrate the advantage of matching the signal's group delay with the generalized time-shift covariance property of a given class of QTFRs, and to demonstrate that mismatch can cause significant distortion.