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Journal Articles Journal of Fourier Analysis and Applications Year : 2020

Phase retrieval for wide-band signals

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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Dates and versions

hal-02124457 , version 1 (09-05-2019)
hal-02124457 , version 2 (06-05-2020)

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Philippe Jaming, Karim Kellay, Rolando Perez Iii. Phase retrieval for wide-band signals. Journal of Fourier Analysis and Applications, 2020, 26, pp.54. ⟨hal-02124457v2⟩

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