Abstract

Fractional calculus studies the possibility of using non-integer derivatives and integral calculus. The are two main definitions or formulations for " Fractional derivative " and " Fractional integral " the first one was developed by Grunwald-Letnikov and the other one by Riemann-Liouville [1]. The Grunwald-Letnikov approach allows to take the derivative of a function a non-integer number of times, allowing its application to numerical methods for signal processing. Fractional derivatives have been successfully applied to different fields such as automatic control [5, 6], physics' string theory [2], signal processing [4] and more recently it has been applied for seismological studies [3]. On the other hand, the Blood pressure (BP) is the pressure of circulating blood on the walls of blood vessels, the arterial blood pressure has a very well-known waveform. The photoplethysmogram (PPG) is a volumetric measurement of an organ. A PPG is often obtained by using a pulse oximeter which illuminates the skin and measures changes in light absorption. In this work we apply the computational Fractional derivatives of Grunwald-Letnikov to process the Photoplethysmography (PPG) signal and when the α parameter is adjusted, the result correspond to the fitted waveform of the finger Arterial Pressure (fiAP). The results shows a low error, indicating that fractional derivatives are useful and they are an effective method to determine a person's blood pressure.