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.