No abstract

This study investigates the phase retrieval problem for wideband 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.2010 Mathematics Subject Classification. 30D05, 30H10, 42B10, 94A12.