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.
La presente investigación tuvo el propósito de constatar estadísticamente la efectividad psicoterapéutica de un modelo de intervención focalizado y de orientación psicoanalítica (ESPORA) sobre el desempeño académico de estudiantes universitarios de la Facultad de Ciencias de la Universidad Nacional Autónoma de México. Específicamente en el análisis de sus promedios y el número de materias inscritas y aprobadas. Se realizó una comparación del comportamiento de ambas variables antes y después del tratamiento en dos grupos de estudiantes, 432 que fueron atendidos y concluyeron el tratamiento y 204 que solicitaron el servicio, pero no lo recibieron. Se aplicó el estadístico Wilcoxon-Mann-Whitney y se obtuvo que entre ambos grupos existen diferencias significativas, de lo cual se puede inferir que el modelo es eficaz y señala la necesidad de institucionalizar este tipo de modelo en espacios universitarios con el objetivo de mejorar su vida académica y evitar la deserción escolar.
In our research on the density fluctuations of a supersonic jet we were confronted with a quite difficult problem. In the power spectrum obtained either with a spectrum analyzer, the peaks of the two of the modes that we wanted to identify overlapped. We needed to find a signal processing method that would resolve the two main frequencies. We made a thorough investigation of several methods and thought that parametric periodograms were the appropriate tool. The use of parametric periodograms in signal processing requires constant training. The proper application of this tool depends on the determination of the number of parameters that has to be used to best model a real signal. The methods generally used to determine this number are subjective, depending on trial and error and on the experience of the user. Some of these methods rely on the minimization of the estimated variance of the linear prediction error , as a function of the number of parameters n. In many cases, the graph vs n doesn't have a minimum, and the methods cannot be used.In this paper, we show that there is a strong relationship between and the frequency resolution 2 wpThat is, as we modify f Δ , we obtain graphs of vs n that present at least one minimum. The spectrum obtained with this optimal number of parameters, always reproduces the frequency information of the original signal. In this paper, we present basically the signal processing of the data obtained in a Rayleigh scattering experiment on a supersonic jet that has also been designed by the authors.2 wp σ
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