WAVELET SMOOTHING OF EVOLUTIONARY SPECTRA BY NONLINEAR THRESHOLDING

We consider wavelet estimation of the time-dependent (evolutionary) po wer spectrum of a locally stationary time series. Hereby, wavelets are used to provide an adaptive local smoothing of a short-time periodogr am in the time-frequency plane. For this, in contrast to classical non parametric (linear) approaches, we use nonlinear thresholding of the e mpirical wavelet coefficients. We show how these techniques allow for both adaptively reconstructing the local structure in the time-frequen cy plane and for denoising the resulting estimates. To this end, a thr eshold choice is derived which results into a near-optimal L(2)-minima x rate for the resulting spectral estimator. Our approach is based on a 2-d orthogonal wavelet transform modified by using a cardinal Lagran ge interpolation function on the finest scale. As an example, we apply our procedure to a time-varying spectrum motivated from mobile radio propagation. (C) 1996 Academic Press, Inc.