An application of fuzzy fractional partial differential equations on heart sound signal denoising

Subject Areas : Statistics

farnoosh karimi ¹ , Tofigh Allahviranloo ² , Saeed Abbasbandy ³

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Imam Khomeini International University (RA), Qazvin, Iran

Received: 2020-04-17 Accepted : 2021-05-15 Published : 2022-01-21

Keywords: کاهش نویز, معادلات دیفرانسیل جزئی فازی, مشتق از مرتبه کسری, سیگنال صدای قلب,

Abstract :

Cardiovascular system is a permanent source of information which incorporate to declaration of Cardiovascular diseases. The existence of available valid data is the main part of any research study. Today, in the field of human life study, experimental data by means of different issues are always deviated from their actual values not only in measurement errors but also it is appeared due to the measuring concept. Composing of heart signal, as a real example of signals, with noise signal causes ambiguity in which classical available methods become disable in correct processing and interpretation of these signals. This paper is focused on proposing an algorithm in signal noise reduction of heart sound signal at pre-processing step. This novel de-noising method of heart sound signal is established on arbitrary order fuzzy partial differential equations. Fuzzification is done due to eliminating of absolute boundaries. The propose algorithm of noise reduction is examined by adding Gaussian white noise to the normal heart sound signal without any noise. De-noising method is implemented after presenting the model concept. Attaining the (FFPDE) filter is including the following steps: the filter matrix is defined after using the backward Euler scheme to discretize the fuzzy differential equation. The results indicated that using of fuzzy fractional partial differential equations was completely effective in de-noising of heart sound signals.

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