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# Understand the fillter function throughout the solved differential equations

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#### matin-kh

##### Member level 3
Hi,

The aim is measuring Vecg through a capacitance sensor in the pictures below and the equations are written down, in the paper related to these pictures says:
"The first term on the right hand side of Eq. 1, s(t), shows that the signal of interest Vecg(t) is filtered by the system and that the filter varies dynamically with Cc(t), introducing a distortion of Vecg(t). "
The problem is that I cannot understand the fillter functioan which has recently talked about throughout the equations, "the signal of interest Vecg(t) is filtered by the system and that the filter varies dynamically with Cc(t)".

Thanks

Do you understand what kind of time-dependency for Cc(t) exists and what causes it? Similarly, what is the nature of Vinj(t)?

Without at least an idea about this points, the equations are meaningless.

Do you understand what kind of time-dependency for Cc(t) exists and what causes it? Similarly, what is the nature of Vinj(t)?

Without at least an idea about this points, the equations are meaningless.
Sorry I forgot to say that in equation 1 we assumed Vinj is zero so consider the next equations without Vinj.
Let me explain a bit about this system it is a contactless ECG sensor which measure the ECG from the body without any contact which it means a capacitor is formed between the body and the electrode, and therefor this capacitor (Cc) is varrying randomly becuse of the body motion. Vdc is also the offset wich is formed between the body and electrode.

Cc(t) is the space between the body and the sensor. With different distances between the body and the sensor, different capacitances result for Cc(t).

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