This work addresses the analysis of families of sound signals through linear transformations that map signals to each other. These transformations are modeled as Gabor multipliers, which are defined by point wise multiplication with a given transfer function in the time-frequency (i.e. Gabor) domain. New approaches for the estimation of such transfer functions, based upon regularized variational approaches are developed. The estimated transfer functions can be used for various purposes in signal analysis and processing. This paper describes an application to sound morphing, in which the regularization parameter plays the role of tuning parameter between input and output signals.