We study in detail two families of q-Fibonacci polynomials and q-Lucas
polynomials, which are defined by non-conventional three-term recurrences. They
were recently introduced by Cigler and have been then employed by Cigler and
Zeng to construct novel q-extensions of classical Hermite polynomials. We
show that both of these q-polynomial families exhibit simple transformation
properties with respect to the classical Fourier integral transform
