Electrical – Convert PWM to Analog using a DAC chip in order to emulate a Potentiometer for audio

Although one could use a simple RC filter, I think one would do better to use some sort of digital filtering. The time scales you're looking at look well within the range of what a processor could handle. I would suggest that your best bet is probably to do something like sample the input pin once per millisecond and keep track of how many times the input has been low during each somewhat longer time interval (maybe one second or five seconds), and then use a digital FIR filter to add up those readings. A simple way to perform the filter FIR filter is to scale up each reading so as to be a bit short of the full range of a 16- or 32-bit integer, and then do something like (pseudo-code):

temp = new_reading
for each item in an array
  new_temp = (temp + array_item)/2
  array_item = temp
  temp = new_temp
loop  

The final value of new_temp will represent a low-pass filtered value of the input; one can vary the number of seconds per reading and the length of the array to adjust the filter characteristics. Note that if one uses e.g. a sampling interval of two seconds and an array that's 16 elements long, only the last 32 seconds of input will be considered in producing the output (meaning that the output will fully respond to any change in input conditions within 32 seconds) but relatively "stable" input conditions will yield a relatively stable output (much more stable than with an RC filter that converges reasonably fast).

I think you've missed some of the limitations of the circuit. In effect, it takes a 5-volt PWM signal, low-pass filters it, then subtracts 2.495 volts to get the output voltage. Since the PWM signal can have a DC component in the range 0 to 5 volts, the output range is -2.5 to 2.5 volts. Its advantage over a simple RC filter on the PWM output is that a) it allows bipolar output, and b) with a 2-pole response it allows a better tradeoff of PWM switching frequency rejection vs. response time for changes in PWM duty cycle. Oh yes, and it's also cheap.

Note, though, that the accuracy of the output is only as good as the accuracy of both the 5-volt and 0-volt levels of the PWM signal. If you want the output to be accurate to 1 mV, the PWM high and low levels must both be accurate to within 1 mV.

There's no free lunch here. For what you're doing, I'd guess you'd be better off using the LM431 as a simple 2.495 reference, then use an analog switch driven by the PWM followed by a multi-pole filter. The more poles in the filter the sharper the cutoff frequency and the faster the response to duty cycle changes for a given level of switching frequency ripple. More poles means more complexity in the filter, but that's the price you pay. The filter could also incorporate the 0.8 gain you want to produce a 0 to 2 volt swing.