Phase Retrieval for Wide Band Signals

This study investigates the phase retrieval problem for wideband signals. More precisely, we solve the following problem: given f ∈ L
²
(ℝ) with Fourier transform in L
²
(ℝ, e
^2c|x|
dx) we determine 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 translate the problem into a phase retrieval problem for functions in Hardy spaces on the disc and use the inner-outer factorization.