On Time-Frequency Resolution of Signal Properties using Parametric Techniques

The problem to track time-varying properties of a signal is studied. The somewhat contradictory notion of “time-varying spectrum” and how to estimate the “current” spectrum in an on-line fashion is discussed. The traditional concepts and relations between time- and frequency resolution are crucial for this problem. An adaptive estimation algorithm is used to estimate the parameters of a time-varying autoregressive model of the signal. It is shown how this algorithm can be equipped with a feature such that the time-frequency resolution trade-off favors quick detection of changes at higher frequencies and has slower adaptation at lower frequencies. This should be an attractive feature and similar to, for example, what wavelet transform techniques achieve for the same problem