  We construct a calculus for generalized $\mathbf{SG}$ Fourier integral
operators, extending known results to a broader class of symbols of
$\mathbf{SG}$ type. In particular, we do not require that the phase functions
are homogeneous. We also prove the $L^2(\mathbf{R}^{d})$-boundedness of the
generalized $\mathbf{SG}$ Fourier integral operators having regular phase
functions and amplitudes uniformly bounded on $\mathbf{R}^{2d}$.
