A Family of Optimal Window Functions for Spectral Analysis with the Spectrum Sidelobe Falloff Rate Multiple of 12 dB per Octave

A synthesis problem is solved for low-order windows with the sidelobe spectrum falloff rate equal to 12 n decibel per octave (dB/oct), where n is an integer, that are optimal by the criterion of the minimum highest spectrum sidelobe level over a given frequency region outside the main lobe. To obtai...

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Bibliographic Details
Published in:Journal of communications technology & electronics 2020-05, Vol.65 (5), p.502-515
Main Authors: Zaytsev, G. V., Khzmalyan, A. D.
Format: Article
Language:English
Subjects:
Communications Engineering
Engineering
Fourier series
Networks
Sidelobes
Spectrum analysis
Synthesis
Theory and Methods of Signal Processing
Trigonometric functions
Window functions
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Summary:A synthesis problem is solved for low-order windows with the sidelobe spectrum falloff rate equal to 12 n decibel per octave (dB/oct), where n is an integer, that are optimal by the criterion of the minimum highest spectrum sidelobe level over a given frequency region outside the main lobe. To obtain this sidelobe falloff rate, it is proposed to synthesize the windows in the form of a portion of the Fourier series in terms of cosine functions with an odd number of half-waves along the observation interval. A synthesis method for the optimal functions with verification of the solution is developed. Order 3 to 6 windows with sidelobe falloff rates 12, 24, and 36 dB/oct are synthesized and their parameters are presented.
ISSN:1064-2269
1555-6557
DOI:10.1134/S1064226920050137