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.

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

El estudio de la refracción de la luz es un fenómeno estudiado en los laboratorios de óptica de la carrera de física e ingeniería y profesiones afines. El estudio, la instrumentación y la técnica han variado muy poco desde hace décadas, por consiguiente, el error de medición sigue siendo los mismos. Entre las variables que se miden directamente durante el desarrollo y estudio de dicho fenómeno se encuentran: La distancia entre la rejilla de difracción y la pantalla donde se proyecta el fenómeno de difracción (D), una segunda medida es la longitud entre un máximo de intensidad de luz hasta donde comienza a incrementar la intensidad del segundo punto luminoso consecutivo (y), y una tercera variable es la medición indirecta del ancho de la rejilla de difracción (a). De los parámetros mencionados es la distancia y la que ocasiona mayor incertidumbre en el resultado dado que esta variable es dependiente del observador o experimentador. En este trabajo se presenta una propuesta innovadora en donde este valor es posible evaluarlo directamente de una gráfica cuyos datos son adquiridos empleando un osciloscopio; los resultados obtenidos mediante el procedimiento descrito en el presente trabajo proporcionan además de resultados con menor incertidumbre, muestran el comportamiento de intensidades de la luz difractada.

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Students of physics, engineering and related majors; generally, do not know the usefulness and applications of transforming a signal from the time domain to the frequency domain. The mathematics that makes possible this transformation is well known to senior students of the majors, but vaguely applied in teaching laboratories. The main phenomena that could provide us with frequency information, the pendulum and the spring, are minimized by focusing only on obtaining the mathematics dictated in books.  The pendulum is the most studied physical system in teaching laboratories from precollege up to college levels; this phenomenon is analyzed mathematically in most of the related literature in the area of Physics and Engineering. It is an introduction to the wave phenomenon. However, teaching paradigms, focus on the plain demonstration that periods are invariant to suspended masses, if and only if the oscillation is within angles not greater than 10 degrees from their normal. The use of technologies, computational and electronic, also focuses on the demonstration of such assertion. In the present work, a mechanical-electrical system was designed that allows to observe, in real time, on the screen of an oscilloscope, the swinging behavior of a pendulum. This system makes evident that the swing movement of a pendulum can be described by a sine function, but also with this same system, and with the help of a digital oscilloscope, it is possible to simultaneously observe the signal generated in the temporal domain and in the frequency domain. This innovation not just breaks the paradigms of teaching but also promotes an alternative to valuable observations promotes understanding.