In this study, some mathematical relations have been derived for the useful parameters of fixed window functions in fractional Fourier transform (FRFT) domain. These reported expressions are also verified with the simulation studies. The FRFT provides an important extension to conventional Fourier transform with an additional degree of freedom by which these parameters of window functions can be controlled while inherent time domain behavior of the windows remains intact. The behavior of fixed windows on time-frequency plane has been varied by varying the FRFT order. The obtained variability in the window functions has been applied in the designing of FIR filters.