In this correspondence, two different window function families, namely, the first-order Bessel (I1-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, have been considered. Closed-form expressions have been derived/computed, which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc. Simple expressions relating to mainlobe width and maximum sidelobe level have been given for the two families considered. The results obtained have been compared to that obtained by Kaiser and Schafer in the case of zeroth-order Bessel (I0-sinh) family. I0-sinh window for spectrum analysis,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 105-107, Feb. 1980. © 1989 IEEE