SHAPING FREQUENCY-DEPENDENT TIME RESOLUTION WHEN ESTIMATING SPECTRAL PROPERTIES WITH PARAMETRIC METHODS

The problem of tracking time-varying properties of a signal is studied . The somewhat contradictory notion of ''time-varying spectrum'' and h ow to estimate the ''current'' spectrum in an on-line fashion is discu ssed. The traditional concepts and relations between time and frequenc y resolution are crucial for this problem. We introduce two definition s for the time resolution of filters, essentially measuring the effect ive number of past data that are used to form the estimate. In, for ex ample, wavelet transform techniques, frequency-dependent time resoluti ons are used so that fewer data are used at higher frequencies, thus e nabling faster tracking of high-frequency components (at the price of worse frequency resolution). The main contribution of the paper is to show how this same feature can be introduced when estimating spectra v ia a time-varying, autoregressive model of the signal. This is achieve d by a special choice of nominal covariance matrix for the underlying parameter changes.