To know what value of capacitor and resistor you want, you will need to think about the response speed you need to achieve. Looking at the waveform, it looks like you get a pulse every few seconds, and the pulses last tens of milliseconds. This is pretty slow, so:
- The analog signal will be much slower than your pulse rate. You should expect the analog signal to take about a minute to settle when the pulse rate changes.
- You will need to choose pretty large values of resistor and capacitor. The time constant of an RC filter in seconds is the product of the resistance in Ohms and the capacitance in Farads.
Since you're looking for something in the order of a minute, I'd start with 12k ohms, and 4700uF. See how that works. If you need a slower response, then use a larger resistor.
Here's what it looks like with 12k and 4700uF:
There are 0.1s pulses every 2 seconds over the course of 2 minutes. As you can see, it hasn't really settled, even after two minutes, and the variation in the analog signal is still about 5%.
With a smaller resistor, you can have faster settling time, but more variation.
With a larger resistor, you can have slower settling time, but less variation.
I don't know if this is an option, but have you considered using a microcontroller to read these signals? What will be reading the analog voltage? If it was going to be an ADC and a microcontroller, I would forget about the ADC, and just let the MCU take care of it. These pulses are so slow that even a computer made out of cog wheels could reliably sample them.