A new efficient approach to the design of parametric windows with arbitrary sidelobe profiles

Abstract

Based on a simple variable transformation in the spectral domain, a new method to parametrize any window in the same way as Kaiser–Bessel or Dolph–Chebyshev windows is presented, allowing a very flexible trade-off between the width of the main lobe and the height of the sidelobes. The derivation of the method is a generalization of the procedure used for the design of Kaiser–Bessel window and van der Maas function, which is related to the Dolph–Chebyshev window. The properties of this spectral transformation are studied. New bases of functions are presented, which can be used to easily design families of windows having a specific asymptotic decrease rate of the sidelobes. Links are made between this work and windows found in the literature.