  In this paper, we show that sparse signals f representable as a linear
combination of a finite number N of spikes at arbitrary real locations or as a
finite linear combination of B-splines of order m with arbitrary real knots can
be almost surely recovered from O(N^2) Fourier intensity measurements up to
trivial ambiguities. The constructive proof consists of two steps, where in the
first step the Prony method is applied to recover all parameters of the
autocorrelation function and in the second step the parameters of f are
derived. Moreover, we present an algorithm to evaluate f from its Fourier
intensities and illustrate it at different numerical examples.
