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Five constructive methods for recovering the symbol of a time-frequencylocalization operator with non-binary symbol are presented, two based onearlier work and three novel methods. For the two derivative methods which havepreviously been applied to binary symbols, we propose a changed symbolestimator and provide additional estimates that show how we can recovernon-binary symbols. The three novel methods each have their own advantages andare all applicable to non-binary symbols. Two of them rely on prescribing theinput of the localization operator and examining the output, allowing fortargeting of the part of the symbol one wishes to recover while the last onerelies on spectral information about the operator. All five methods are alsoimplemented numerically and evaluated with the code available.

Five ways to recover the symbol of a non-binary localization operator