Phase retrieval for wide-band signals

2019/05/10 by Jaming, Philippe, Kellay, Karim, Perez, Rolando · 1 citation
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Electrical engineering #FOS: Mathematics #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1905.04095

Abstract

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.

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