  A Lee-Yang polynomial $ p(z_{1},\ldots,z_{n}) $ is a polynomial that has no
zeros in the polydisc $ \mathbb{D}^{n} $ and its inverse $
(\mathbb{C}\setminus\overline{\mathbb{D}})^{n} $. We show that any real-rooted
exponential polynomial of the form $f(x) = \sum_{j=0}^s c_j e^{\lambda_j x}$
can be written as the restriction of a Lee-Yang polynomial to a positive line
in the torus. Together with previous work by Olevskii and Ulanovskii, this
implies that the Kurasov-Sarnak construction of $ \mathbb{N} $-valued Fourier
quasicrystals from stable polynomials comprises every possible $ \mathbb{N}
$-valued Fourier quasicrystal.
