Windowing applied to a given signal is a technique commonly used in signal processing\nin order to reduce spectral leakage in a signal with many data. Several windows\nare well known: hamming, hanning, beartlett, etc. The selection of a window is\nbased on its spectral characteristics. Several papers that analyze the amplitude and\nwidth of the lobes that appear in the spectrum of various types of window have been\npublished. This is very important because the lobes can hide information on the frequency\ncomponents of the original signal, in particular when frequency components\nare very close to each other. In this paper it is shown that the size of the window can\nalso have an impact in the spectral information. Until today, the size of a window has\nbeen chosen in a subjective way. As far as we know, there are no publications that\nshow how to determine the minimum size of a window. In this work the frequency\ninterval between two consecutive values of a Fourier Transform is considered. This\ninterval determines if the sampling frequency and the number of samples are adequate\nto differentiate between two frequency components that are very close. From\nthe analysis of this interval, a mathematical inequality is obtained, that determines in\nan objective way, the minimum size of a window. Two examples of the use of this\ncriterion are presented. The results show that the hiding of information of a signal is\ndue mainly to the wrong choice of the size of the window, but also to the relative\namplitude of the frequency components and the type of window. Windowing is the\nmain tool used in spectral analysis with nonparametric periodograms. Until now,\noptimization was based on the type of window. In this paper we show that the right\nchoice of the size of a window assures on one hand that the number of data is enough\nto resolve the frequencies involved in the signal, and on the other, reduces the number\nof required data, and thus the processing time, when very long files are being\nanalyzed.
Loading....