Tailoring of Minimum Sidelobe Cosine-Sum Windows for High-Resolution Measurements



Hans-Helge Albrecht*
Physikalisch-Technische Bundesanstalt (PTB), Berlin, Germany


© 2010 Hans-Helge Albrecht.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Physikalisch-Technische Bundesanstalt (PTB), Abbestraße 2-12, 10587 Berlin, Germany; Tel: +49 30 3481 7311; Fax: +49 30 3481 7490; E-mail: hans-helge.albrecht@ptb.de


Abstract

Cosine-sum windows with minimum sidelobes (minimum sidelobe windows) have good properties in terms of peak sidelobe level (PSL) and equivalent noise bandwidth (ENBW). But neighboring windows (the number of coefficients differ by one) have quite large PSL differences. If, for a special data analysis, the PSL of the window should not exceed a given value, then often windows with a much lower PSL than specified have to be used. Due to increasing ENBW in the case of decreasing PSL, this leads, amongst others, to more uncertainty in the determination of signal amplitudes.

This article describes how to design modified minimum sidelobe windows which have similar properties to minimum sidelobe windows for a given PSL. Their ENBW were, however, traded off against PSL. Using such a design, windows can be created exactly for a given value of PSL at small ENBW. The adjustment of the asymptotic decay of the sidelobes and the determination of the window coefficients will be done without solving linear systems of equations to avoid known numerical problems. By using the proposed algorithm, more than 6000 windows with PSL values greater than -350 dB were created. The parameters and coefficients of selected windows will be given in the article.

Keywords: Window function, spectral analysis, Fourier transform, Signal processing.