Exponential Window Family

Abstract

In this paper we propose a new class of 2-parameter adjustable windows, namely Exponential window, based on the exponential function [1,2]. The Exponential window is derived in the same way as Kaiser window was derived, but our proposed window is more computationally efficient because in its time domain function it has no power series expansion. First, the spectrum design equations for the Exponential window are established, and the spectral comparisons are performed with Cosh, Kaiser and ultraspherical windows. The proposed window is compared with Cosh and Kaiser windows, and the results show that for the same window length and mainlobe width the Exponential window provides better sidelobe roll-off ratio characteristic, which may be important for some applications, but worse ripple ratio. The second comparison is performed with ultraspherical window for the same window length, mainlobe width and sidelobe roll-off ratio and the results demonstrate that the Exponential window exhibits better ripple ratio for the narrower mainlobe width and larger sidelobe roll-off ratio, but worse ripple ratio for the wider mainlobe width and smaller sidelobe roll-off ratio.