Phase retrieval for wide-band signals

Philippe Jaming (1) , Karim Kellay (1) , Rolando Perez Iii (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 UP System - University of the Philippines

This study investigates the phase retrieval problem for wide-band signals. We solve the following problem: given f ∈ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x|} dx), we find all functions g ∈ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x| dx}), such that |f (x)| = |g(x)| for all x ∈ R. To do so, we first translate the problem to functions in the Hardy spaces on the disc via a conformal bijection, and take advantage of the inner-outer factorization. We also consider the same problem with additional constraints involving some transforms of f and g, and determine if these constraints force uniqueness of the solution.

Domaines: Analyse classique [math.CA]; Variables complexes [math.CV]; Traitement du signal et de l'image [eess.SP]

Philippe Jaming, Karim Kellay, Rolando Perez Iii. Phase retrieval for wide-band signals. 2019. ⟨hal-02124457v1⟩