  In this paper, we establish quantitative results for sign changes in certain
subsequences of primitive Fourier coefficients of a non-zero Siegel cusp form
of arbitrary degree over congruence subgroups. As a corollary of our result in
degree two case, we get sign changes of diagonal Fourier coefficients. In the
course of our proofs, we also prove results about the non-vanishing of certain
type of Fourier-Jacobi coefficients of a Siegel cusp form and all theta
components of a Jacobi cusp form of arbitrary degree over congruence subgroups,
which may be of independent interest.
