How to calculate voltage change across electrodes in tank of water?

Question

Reposting from https://physics.stackexchange.com/questions/736554/how-to-calculate-voltage-change-across-electrodes-in-tank-of-water because apparently this is an engineering question and not an experimental physics question.

Apologies for the basic question. I am a neuroscience student and not that familiar with physics.

I am delivering a 1 V bipolar sinusoidal stimulus at 842Hz to a tank of deionized water at 26C with two electrodes for one minute. I am also recording from two electrodes with a sampling rate of 20kHz inside that tank approximately 0.3 m away. I would like to calculate the voltage recorded by the recording electrodes that is due to the sinusoidal stimulus as a function of time. However, I am not sure how to go about doing this. I would greatly appreciate any help in calculating this.

My purpose for this is to separate my electrical stimulus from the electric organ discharge produced by a black ghost knifefish in the tank. My recording electrodes pick up both the discharge produced by the fish and the output of my stimulating electrodes. I have chosen the frequency of my electrical stimulus to be within 1-2Hz of the frequency produced by the fish, in hopes of observing a jamming avoidance response by the fish (i.e. the fish shifting its discharge frequency away from the stimulus frequency). This makes it hard to distinguish my stimulus from the fish's discharge in the spectrum view of my data (i.e. after Fourier transforming). Therefore it would be very helpful if I could calculate the voltage recorded by the recording electrodes in response to the stimulus voltage, given the stimulus voltage as a function of time. Then I would be able to subtract out this voltage from my data to get the discharge from the fish. I have recordings from when there is no stimulus, and by merely eyeballing my data I can see that the voltage change in the recording electrodes in response to the stimulus is somewhere around 3-4% of the stimulus voltage. But it would be great if there were a more methodical way to do this.

If more information is needed, let me know and I can try to provide it.

Answer 1

My suggestion is to first measure the response of the tank without the fish. In this way you can determine the transfer function $G(\omega)$ of the tank from the electrodes (input) $U(\omega)$ to your sensors (output) $Y(\omega)$: $$ G(\omega) = \frac{Y(\omega)}{U(\omega)}. $$

If you then measure the response of the tank with the fish, you can substract the (expected) response from the tank and you get the response of the fish $Y_\mathrm{fish} = Y(\omega)-G(\omega)U(\omega)$.

However, in practice your measurements will be polluted with a transient response and noise. Moreover, if you do not use the correct number of samples for the Fourier transform you will also introduce spectral leakage.

To avoid spectral leakage, choose a window length that fits an integer number of periods of your stimulus frequency (this is important as being of by one sample will already introduce spectral leakage). To reduce the effect of the transient, start your window after the transient term has diminished.

I hope this will help designing/performing your experiment.

Answer 2

Not an expert here, but let me start the conversation.

Maybe you can model the current produced by your stimulating electrodes as a current dipole, somehow use Maxwell's equations to get an electric field pattern from the dipole, and then integrate the electric field along a path between your two recording electrodes.

This is similar work to what I did in my undergraduate lab many years ago. I forget it mostly, but if you look up Current Density Imaging (MRI imaging), you may get somewhere.