A method for optimizing the ambiguity function concentration

Hans-Georg Feichtinger (1) , Darian Onchis-Moaca (1) , Benjamin Ricaud (2) , Bruno Torrésani (2) , Christoph Wiesmeyr (1)

1 NuHAG - Numerical Harmonic Analysis Group, Faculty of Mathematics
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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 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 .

Mots clés: time-frequency localization; ambiguity function; STFT multiplier; iterative diagonalization

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Hans-Georg Feichtinger, Darian Onchis-Moaca, Benjamin Ricaud, Bruno Torrésani, Christoph Wiesmeyr. A method for optimizing the ambiguity function concentration. EUSIPCO 2012, European Signal Processing Conference, Aug 2012, Bucarest, Romania. pp.804-808. ⟨hal-00747590⟩