OPTIMUM SIGNAL SYNTHESIS FOR TIME-SCALE ESTIMATION

In signal analysis, the joint estimation of the time-scale parame-ters which can affect a known signal (Doppler effect or scale ef-fect, delay...) may be a problem of interest. An important result has shown that, even if the quality of the time delay estimation is classically given by the inverse spread of the signal spectral den-sity, the quality of the scale estimation only depends on the inverse of the signal spread in Mellin space. This spread has a direct in-terpretation in the time-frequency plane and can be precisely es-timated when duration, bandwidth and relative bandwidth of the signal are known. We propose here to develop two methods of optimum signal synthesis which minimize the variance of the esti-mates given by the Cramer-Rao lower bounds. The first method is based on the stationary phase principle, applied on frequency and Mellin spaces, which allows to construct signals with given auto