A method for optimizing the ambiguity function concentration

Hans Georg Feichtinger, Darian Onchis-Moaca, Benjamin Ricaud, Bruno Torrésani, Christoph Wiesmeyr

Abstract: In the context of signal analysis and transformation in the time-frequency (TF) domain, controlling the shape of a waveform in this domain is an important issue. Depending on the application, a notion of optimal function may be defined through the properties of the ambiguity function. We present an iterative method for providing such optimal functions under a general concentration constraint of the the ambiguity function. At each iteration, it follows a variational approach which maximizes the ambiguity localization via a user-defined weight function F. Under certain assumptions on this latter function, it converges to a waveform which is optimal according to the localization criterion defined by F.