Analytical formulae for reconstruction of certain discrete signals from phase level and line crossings

We provide simple and explicit formulae for reconstructing any member of a class of discrete-time signals from the frequencies at which its Fourier phase crosses any specific level of constant phase or a linear-phase line with integer slope, provided that the number of crossings equals the length of the signal support. Unlike previous closed-form solutions, solution of an ill-conditioned system of linear equations is not required. The associated uniqueness results reduce, in special cases, to previous results for reconstruction from Fourier transform real and imaginary part zero crossings.