RN42/RN41 emitting noise on supply line when connected.

Hi there, I've been working on a project using an electret microphone and a RN42, the problem is when you connect to the bluetooth module, it starts emitting noise on the supply line (the noise has an 800Hz base frequency). The RN41 produces a lot more of noise. Of course all the analog side of the board is disturbed by this noise, I added a 1000uF capacitor to filter out some of it, it is already greatly reduced but still noticeable.

So, is there a way to completely get rid of it?

Thanks.

I was going to suggest an inductor of 1000uH or so but at 800Hz will be about 5 ohms. The cap will be about 1.2 ohms so it might work. More inductance needed. How many mA does the module draw?

Your best bet is to see if you can run the module off of a different power supply than your audio if possible.