ﮐﺎﺭﺑﺮﺩ ﻣﻌﺎﺩﻻﺕ ﺩ ﻳﻔﺮﺍﻧﺴﻴﻞ ﺟﺰﺋﻲ ﮐﺴﺮﻱ ﻓﺎﺯ ﻱ ﺩﺭ ﮐﺎﻫﺶ ﺍﺧﺘﻼﻝ ﺳﻴﮕﻨﺎﻝ ﺻﺪﺍﻱ ﻗﻠﺐ

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

ﻣﻄﺎﻟﻌﺎﺕ ﻋﻠﻤﻲ ﺑﻪ ﻣﻴﺰﺍﻥ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﺩﺍﺩﻩﻫﺎﻱ ﻣﻌﺘﺒﺮ ﺑﺴﺘﮕﻲ ﺩﺍﺭﺩ. ﺍﻣﺮﻭﺯﻩ ﺩﺭ ﺯﻣﻴﻨﻪﻫﺎﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﺗﺤﻘﻴﻘﺎﺕ ﺣﻴﺎﺗﻲ ﺑﺸﺮ، ﻧﻪ ﺗﻨﻬﺎ ﺑﻪ ﺩﻟﻴﻞ ﺧﻄﺎﻫﺎﻱ ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ﺑﻠﮑﻪ ﺑﻪ ﺩﻟﻴﻞ ﺍﺑﻬﺎﻡ ﺩﺭ ﻣﻔﻬﻮﻡ ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ، ﺩﺍﺩﻩﻫﺎﻱ ﺗﺠﺮﺑﻲ ﻫﻤﻴﺸﻪ ﺗﻮﺳﻂ ﺍﻃﻼﻋﺎﺕ ﻧﺎﺩﺭﺳﺖ ﺁﻟﻮﺩﻩ ﻣﻲﺷﻮﻧﺪ. ﺑﻪ ﻋﻨﻮﺍﻥ ﻳﮏ ﻧﻤﻮﻧﻪ ﻭﺍﻗﻌﻲ ﻣﻲﺗﻮﺍﻥ ﺑﻪ ﺍﺩﻏﺎﻡ ﺳﻴﮕﻨﺎﻝﻫﺎﻱ ﺣﻴﺎﺗﻲ ﺍﺯﺟﻤﻠﻪ ﺳﻴﮕﻨﺎﻝ ﻗﻠﺐ ﺑ ﺎ ﻧﻮﻳﺰ ﺍﺷﺎﺭﻩ ﮐﺮﺩ ﮐﻪ ﺩﺭ ﺁﻥ ﺍﺑﻬﺎﻡ ﻣﻮﺟﻮﺩ ﻣﺎﻧﻊ ﺍﺯ ﭘﺮﺩﺍﺯﺵ ﺻﺤﻴﺢ ﺳﻴﮕﻨﺎﻝ ﺑﺎ ﺭﻭﺵﻫﺎﻱ ﮐﻼﺳﻴﮏ ﺷﺪﻩ ﺍﺳﺖ. ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺳﻌﻲ ﻣﺎ ﺑﺮ ﺁﻥ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﻣﺮﺣﻠﻪ ﭘﻴﺶﭘﺮﺩﺍﺯﺵ ﺳﻴ ﮕﻨﺎﻝ، ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺑﺮ ﺍﻱ ﮐﺎﻫﺶ ﻧﻮﻳﺰ ﺳﻴﮕﻨﺎﻝ ﺻﺪ ﺍﻱ ﻗﻠﺐ ﻃﺮﺍﺣﻲ ﮐﻨﻴﻢ. ﺭﻭﺵ ﺟﺪﻳﺪ ﺣﺬﻑ ﻧﻮﻳﺰ ﺍﺯ ﺳﻴ ﮕﻨﺎﻝﻫﺎﻱ ﺻﺪﺍﻱ ﻗﻠﺐ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻌﺎﺩﻻﺕ ﺩﻳﻔﺮﺍﻧﺴﻴﻞ ﺟﺰﺋﻲ ﻓﺎﺯﻱ ﺍﺯ ﻣﺮﺗﺒﻪ ﮐﺴﺮﻱ )FFPDE( ﺟﻬﺖ ﺩﺳﺘﻴﺎﺑﻲ ﺑﻪﺩﻗﺖ ﺑﺎﻻ ﺍﺭﺍﺋﻪ ﻣﻲﺷﻮﺩ. ﻓﺎﺯﻱ ﺳﺎﺯﻱ ﺑﺮﺍﻱ ﺍﺯ ﺑﻴﻦ ﺑﺮﺩﻥ ﻣﺮﺯﻫﺎﻱ ﻣﻄﻠﻖ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﺍﺳﺖ. ﺍﻟﮕﻮﺭﻳﺘﻢ ﺑﺮ ﺭﻭﻱ ﺳﻴ ﮕﻨﺎﻝ ﺻﺪ ﺍﻱ ﻗﻠﺐ ﻧﺮﻣﺎﻝ ﺑﺪﻭﻥ ﻧﻮﻳﺰ ﺑﺎ ﺍﻓﺰﻭﺩﻥ ﻧﻮﻳﺰ ﺳﻔ ﻴﺪ ﮔﺎﻭﺳﻲ ﻣﻮﺭﺩ ﺁﺯﻣﺎﻳﺶ ﻗﺮﺍﺭ ﻣﻲﮔﻴﺮﺩ. ﭘﺲ ﺍﺯ ﻣﻌﺮﻓﻲ ﻭ ﺍﺭﺍﺋﻪ ﻣﺪﻝ، ﺣﺬﻑ ﻧﻮﻳﺰ ﻣﺒﺘﻨﻲ ﺑﺮ ﺭﻭﺵ ﺍﻧﺠﺎﻡ ﻣﻲﮔﻴﺮﺩ. ﺗﺤﻘﻖ ﻓﻴﻠﺘﺮ FFPDE ﺍﺯ ﻣﺮﺗﺒﻪ ﮐﺴﺮﻱ ﺑﻪﻃﻮﺭ ﮐﻠﻲ ﻣﺮﺍﺣﻞ ﺯﻳﺮ ﺭﺍ ﺷﺎﻣﻞ ﻣ ﻲﺷﻮﺩ؛ ﺍﺑﺘﺪﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯﺟﻤﻠﻪ ﭘﺴﺮﻭ ﺍﻭﻳﻠﺮ ﻭ ﮔﺴﺴﺘﻪ ﺳﺎﺯﻱ، ﻣﻌﺎﺩﻟﻪ ﺩﻳﻔﺮﺍﻧﺴﻴﻞ ﻓﺎﺯ ﻱ ﺑﻪ ﺩﺳﺖ ﻣﻲﺁ ﻳﺪ. ﺳﭙﺲ ﻣﺎﺗﺮﻳﺲ ﻓﻴﻠﺘﺮ ﻣﻌﺮﻓﻲ ﻣﻲﺷﻮﺩ. ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ ﺣﺎﮐﻲ ﺍﺯ ﺁﻥ ﺍﺳﺖ ﮐﻪ ﻣﻌﺎﺩﻻﺕ ﺩﻳﻔﺮﺍﻧﺴﻴﻞ ﺟﺰﺋﻲ ﻓﺎﺯﻱ ﺍﺯ ﻣﺮﺗﺒﻪ ﮐﺴﺮﻱ ﺩﺭ ﺗﺸﺨﻴﺺ ﻭ ﮐﺎﻫﺶ ﻧﻮﻳﺰ ﺑﺴﻴﺎﺭ ﮐﺎﺭﺍ ﺍﺳﺖ

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.