Noise when running Arduino close to analogue audio circuit
Arduino PWM signal is about 500Hz, so it will be audible (read: noise) by itself. You could implement a low-pass filter between the PWM pin and your J-FET. A simple RC filter tuned to 5Hz would attenuate a 500Hz signal to -40dB, which probably won't be enough for high quality audio. There are filters with better rejection properties which usually require active components to build. One of the simplest of such filters is the Sallen-Key topology, which can practically double the rejection ratio using a signle active component (opamp).

Another option is to use a simple RC filter, but increase the the PWM frequency (as described here) to achieve high rejection ratio. Eventually, increasing the frequency past the audible range (about 16kHz) will ultimately resolve the noise problem, though I would still use an RC filter to keep the J-FET in linear mode. Apparently, the highest frequency you can achieve at full resolution is 62.5KHz, which is more than enough.