TITLE:
Evaluation of the Minimum Size of a Window for Harmonics Signals
AUTHORS:
José Manuel Alvarado Reyes, Catalina Elizabeth Stern Forgach
KEYWORDS:
Minimum Size of a Window, Windowing, Spectral Resolution
JOURNAL NAME:
Journal of Signal and Information Processing,
Vol.7 No.4,
October
11,
2016
ABSTRACT: Windowing applied to a given signal is a
technique commonly used in signal processing in order to reduce spectral
leakage in a signal with many data. Several windows are well known: hamming,
hanning, beartlett, etc. The selection of a window is based on its spectral
characteristics. Several papers that analyze the amplitude and width of the
lobes that appear in the spectrum of various types of window have been
published. This is very important because the lobes can hide information on the
frequency components of the original signal, in particular when frequency
components are very close to each other. In this paper it is shown that the
size of the window can also have an impact in the spectral information. Until
today, the size of a window has been chosen in a subjective way. As far as we
know, there are no publications that show how to determine the minimum size of
a window. In this work the frequency interval between two consecutive values of
a Fourier Transform is considered. This interval determines if the sampling
frequency and the number of samples are adequate to differentiate between two
frequency components that are very close. From the analysis of this interval, a
mathematical inequality is obtained, that determines in an objective way, the
minimum size of a window. Two examples of the use of this criterion are
presented. The results show that the hiding of information of a signal is due
mainly to the wrong choice of the size of the window, but also to the relative
amplitude of the frequency components and the type of window. Windowing is the
main tool used in spectral analysis with nonparametric periodograms. Until now,
optimization was based on the type of window. In this paper we show that the
right choice of the size of a window assures on one hand that the number of
data is enough to resolve the frequencies involved in the signal, and on the
other, reduces the number of required data, and thus the processing time, when
very long files are being analyzed.