Published
Two algorithms for estimating the period of a discrete signal
Dos algoritmos para estimar el periodo de una señal discreta
Keywords:
Frequency estimation, frequency measurement, periodic functions, power system monitoring, signal reconstruction (en)estimación de frecuencia, medida de frecuencia, funciones periódicas, monitoreo de sistemas de potencia, reconstrucción de señales (es)
In this paper, we present two algorithms for approximating a period given a discrete data set. These algorithms superimpose two consecutive sections of the data for several candidate periods. The first algorithm counts the number of shuffling points per candidate period, whereas the second algorithm computes a distance between points when sorted by time. The best candidate period maximizes the number of shuffling points in the first algorithm, whereas the second algorithm minimizes the distance between points. The experimental validation with noiseless data demonstrates that the relative error for the estimations is less than half of the sampling period and shows that this error does not depend on the harmonic content, as normally occurs with algorithms that estimate a period. The application of the algorithms demonstrates that they properly track the frequency of a power grid and accurately estimate the period of a Van der Pol oscillator, which serves to confirm their applicability to real-time problems.
En este artículo se presentan dos algoritmos para estimar el periodo de una señal, dado un conjunto de datos discretos, estos algoritmos superponen dos secciones de datos a varios periodos. El primer algoritmo cuenta el número de puntos que se mezclan por cada periodo, mientras el segundo, calcula la distancia entre los puntos cuando se ordenan por tiempo. De esta manera, el mejor candidato para periodo maximiza el número de puntos que se mezclan en el primer algoritmo, mientras que en el segundo, minimiza la distancia entre puntos.
La validación experimental con señales sin ruido, demuestra que el error relativo de las estimaciones cae por debajo de la mitad del periodo de muestreo, y a su vez, muestra que ese error no depende del contenido armónico de la señal, como ocurre con los algoritmos para estimar periodo. La aplicación de los algoritmos demuestra que pueden seguir la frecuencia de un sistema de potencia y además, pueden aproximar el periodo de un oscilador Van der Pol, lo cual sirve para confirmar que estos algoritmos se pueden aplicar para solucionar problemas en tiempo real.
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Copyright (c) 2014 José Danilo Rairán Antolines
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