Contributed talk: phase retrieval for wide band signals
This study investigates the phase retrieval problem for wide-band signals. We solve the following problem: given f∈L2(\R) with Fourier transform in L2(\R,e2c|x|dx), we find all functions g∈L2(\R) with Fourier transform in L2(\R,e2c|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. This was a joint work with Philippe Jaming and Karim Kellay.