Optimal parameters in modulated Laguerre series expansions

The harmonically modulated Laguerre functions constitute an orthonormal basis in the Hilbert space of square-integrable functions on R/sup +/. This basis comprises three free parameters, namely a modulation, a scale and an order factor. In practice, we are interested in series expansions that are as compact as possible. The free parameters can be used as the means to obtain a compact series expansion for a given function. As the compactness criterion the first-order moment of the energy distribution in the transform domain is chosen. In that case, the optimum compactness parameters can be given in a simple analytic form depending on signal measurements only.