Double insulated is different – but the same.
Just as with the earthed components, the system needs its own reference ground and all the components in the system need to have a connections to that. Usually in Hi-Fi the screen of the RCA connections provides this connection between all the components.
Here's a thing though. Each power supply in the system will have an individual characteristic and will be capacitively, or otherwise, linked to the chassis and the incoming mains in one way or another. This means there is a wild voltage induced on the chassis. When you plug an RCA input to an amp with the amp on (not recommended) when the single centre wire connects, but before the ground part of the RCA makes contact, there is usually a nice hum or noise. This is not interference from the air, I assure you (there just isn't that amount of energy in the air unless you system is inside a power station!). What you are hearing there is the difference in potentials between the two bits of kit. Don't forget they are floating with respect to earth as they are double insulated. Not only is it floating at a random voltage induced from its own power source connection to the mains, but the chassis is also floating and able to pick up noise form any mains supply in the vicinity that is radiating. This is not RF, this is low frequency induced energy
When the RCA connects, all becomes quiet as the RCA ties the two chassis electrically together.
All fine. Well no. There still exists a potential between the chassis, the RCA screen has linked them so the difference in voltage is shorted out. But that means that there is an eddy current flowing in the screen. How close is the screen to the signal cable in the RCA wire? Very. Very close, and that does mean the eddy currents flowing between the chassis throught he screens due to induced pick up is capcaitively linking to the signal cable itself and raising the noise floor. You can't get away from it!... but you can mitigate it. In large professional audio and video installations (stadia, film and audio studios, theartres etc) this is a very real problem on an un-ignorable scale that has to be managed in the desing for the system cable layout. In hi-fi systems it is there, just not as prevalent becuase the scale is so much smaller.
Normally this is not considered a big deal, but on high performance systems it does reduce imagary, and there are the techniques that can improve image by considering this aspect of power supplies, grounding and interecoonections. If, for example, you connect all screens at one end only (I would suggest the Amp) and bind everything with one, nice thick gauge bonding wire, then all possible paths of eddy curretns are removed, except for in the binding system ground wire (We call his a 'technical earth'). It's a shame the old practice of providing a chassis grounding screw (prevalent in the 50's and 60's) was lost- those guys knew what they were about!
This system ground need not be connected to mains earth, though if done safely it does give the system a real reference to the real ground that you, I and the rest of the world share. What I mean is that the entire system will not be then floating at what ever voltage gets induced on it through capactive linkage to the incoming mains throughthe power supplies. Though- if done- this must always be done by a qualified, competent electrician. (I need to cover my .... here). All the cables I designed for Studio Connections do not have a screen, but they do have a ground wire which is designed to provide the ground linkage with absolute minimal linkage to the signal wire. And it really works- I nearly fell of my chair when I first tried it because I thought cables I used to use were already reaching the zenith of performance. Fact is its simple physics, and one point that we- as an industry-managed to over look. I have a great quote from David Wilson of Wilson saying it works, - in fact he said about the Studio Connections interconnect cable ' The results were sensational'.
Ok – a mild plug, but I will balance it by saying that I have made cables for a lot of people, From Kelsey (pro audio systems for theatres, concert Halls) Abbey Road , - but its Studio Connections thatare my high end favourites as I wanted to reach the zenith bearing in mind the physics and materials that we know about.
Now- back to mains filters. Even if the components are said to be floating (as double insultated systems nominaly sre), there is quite significant inductive linking between the chassis and the mains (as shown earlier) – and there is also a resistive linkage – albeit mega ohms, throught the insutation. Double isutlated in really about the mains saftey insulation, not about perfect electronic isolation. It is therefore best to make sure the same version of the mains voltage is arriving at each bit of equipment to ensure that there is minimal differential between each bit of kit. Separate filters to each piece of kit will increase the noise differential. One mains filter that then stars out to all the kit is good, provided of course you have checked it is very capable of providing the system current.
And of course, if you use the carbon screen cables, this helps capacitively shunt and dissipate out any nasties that happen to be coming up the mains as well.
Technically…by the way, you referred to shunt filtering. Herein is the main difference between the metal braid screen and the carbon loaded types, - one shunts (to where….?) the other shunts and dissipates, so it's more like an RC than just a C with no R.
Believe me- system ground is one of the most ignored and assumed quantities and yet about the most important in high performance systems.
Hope this helps a little more