To the left is a small circuit that generates a 0 V to +5 mV square wave at 1 Hz, to somewhat simulate a heart rate.

On the breadboard to the left is a voltage divider to prive the virtual ground at half of the battery voltage.

Then is the AD620 inamp for the initial amplification.

Then I used a TL082 for both an additional amplification as well as summing, using a potentiometer to shift the level up or down.

Then the signal is read by the Arduino which simply reads the analog signal and translates it to a 0-1023 integer value (where 1023 would mean the signal is at 5 V) and sends it to the laptop over serial.

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Possible improvements: