The Gabor transform of a signal creates a time-frequency representation of physical data which can be directly manipulated through multiplication by symbols, analogous to the action of pseudodifferential operation and their representation through symbols in the time-frequency domain.

This two-lecture minicourse describes the basics of Gabor transforms and Gabor multipliers, windowing considerations, representation of linear operators including differential operators, and the use of Gabor multipliers in nonstationary filtering, deconvolution, and numerical wave propagation. Some particular imaging applications are described.