A Fourier based algorithm to estimate the period of a sampled signal
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Universidad Distrital Francisco José de Caldas
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Dada una se˜nal muestreada, en general, no es posible calcular su periodo, sino solo una aproximaci´on. En este art´ıculo se propone un algoritmo para aproximar el periodo, basado en la Transformada Discreta de Fourier. Si esa transformaci´on utiliza datos por un m´ultiplo del n´umero de periodos, algunos de sus arm´onicos resultan nulos. As´ı, el mejor candidato a ser un m´ultiplo del periodo es el que minimiza el valor de esos arm´onicos. La validaci´on para datos sin ruido muestra un l´ımite m´aximo para el error de un cuarto del tiempo entre dos muestras consecutivas, mientras que el resultado para se˜nales con ruido demuestra robustez. Como aplicaci´on, el algoritmo es utilizado para estimar el periodo de una se˜nal fisiol´ogica, y el seguimiento de la frecuencia de un sistema de potencia, en tiempo real, lo cual evidencia la versatilidad del algoritmo.
Given a sampled signal, in general, is not possible to compute its period, but just an approximation. We propose an algorithm to approximate the period, based on the Discrete Fourier Transform. If that transformation uses data length for multiples of the true period, some of its harmonics have null value. Thus, the best candidate to be a multiple of the period minimizes the value of those harmonics. The validation for noiseless data shows an upper bound in the error equal to a quarter of the time between two consecutive samples, whereas the result for noisy data demonstrates robustness. As application, the algorithm estimates the period of physiological signals, and tracks the frequency of the power grid in real time, which evidence its versatility
Given a sampled signal, in general, is not possible to compute its period, but just an approximation. We propose an algorithm to approximate the period, based on the Discrete Fourier Transform. If that transformation uses data length for multiples of the true period, some of its harmonics have null value. Thus, the best candidate to be a multiple of the period minimizes the value of those harmonics. The validation for noiseless data shows an upper bound in the error equal to a quarter of the time between two consecutive samples, whereas the result for noisy data demonstrates robustness. As application, the algorithm estimates the period of physiological signals, and tracks the frequency of the power grid in real time, which evidence its versatility
Palabras clave
Period estimation, Physiological signals, Power grid frequency, Discrete Fourier Transform, Estimación del periodo, señales fisiológicas, Frecuencia de un sistema de potencia, Transformada Discreta de Fourier