http://www.diyaudio.com/forums/power-su ... ost4565910
"A battery filters down to DC. Even if the battery has .1 ohm resistance what value capacitor do you need to equal that? Answer infinite.
The definition of capacitance is C=Q/V. The important part of the first derivative is C x dV/dT = i. Now most folks get that F = 1/T. So they assume that if the lowest audio frequency is 20 hertz then dT = .05. As this is a power supply not a series pass use that is too simplistic. The power supply filter capacitor may be recharged 120 times a second but the is an effective series resistance in any power source before the filter capacitor. So instead we need to look at the envelope of the signal. IE when a drummer strikes the drum a surge of power is required for as much as 2 seconds as the note decays. So you would want your power supply not to sag a noticeable amount during that time. Not being noticeable would be around 3% or less. Just to make things a bit tougher on the filter capacitors, maximum low frequency energy in music is around 150 hertz.
So the beat frequency of 30 hertz will show up at some level. As a minimum that should be 30 dB down.
Now adding capacitors to add surge filtering to a battery power supply requires stupidly large capacitors to have any effect. However with virtually all cases the measurable effect will not have any audiable change.
So the only challenge is to make sure your power distribution traces or wiring doesn't screw things up.
As to where to place a rail to rail capacitor, if you are using an op-amp as the output, right across the + & - power pins. This is in addition to the normal capacitors to ground.
Conclusion is that with batteries you are not trying to get rid of power supply noise, you are trying to damp the circuit load noise. This is best done at the noise source. That is where the circuit connects to the rails.