SMOOTH DETECTORS OF LINEAR-PHASE

Functions with (linear) phase depend on (linear) combinations of the i ndependent variables. For example plane waves are functions of a singl e linear combination of the variables. Detection of phase is an import ant problem in seismic velocity analysis and ocean acoustic signal pro cessing, amongst other applications. Robust estimation of phase by loc al optimization requires the construction of smooth objective function als. For this purpose it is useful to characterize those quadratic fun ctionals of functions with linear phase which are smooth in the phase: all such smooth phase detectors are pseudodifferential. Some of these pseudodifferential quadratic forms are globally convex in the phase, hence permit phase estimation using local smooth optimization methods.