I am working with digital amplifiers and from what I can see there is a DC blocking filter that is placed at the start of the signal chain.
DC is not audio and should not be amplified or be present at speakers as DC current can burn the speaker coil. Unwanted DC can also cause problems in the signal processing blocks, be them analog or digital, so the best thing to do is to just filter out out before processing the signal any further. Sometimes a processing block might require a certain DC level to operate properly, so of course the old DC bias must be filtered out before applying a new DC bias, this is done between analog portions in an amplifier and sometimes a small DC bias is added to a digital signal to avoid denormal numbers in processing.
The frequency is arbitrary. It must be high enough to block unwanted DC and drift, but low enough to pass audio with little phase distortion. Basically a rule of thumb is that for a simple analog RC filter, to pass audio down to 20 Hz with little phase change, the RC cutoff frequency needs to be a decade lower so 2 Hz. So a higher order 4 Hz digital filter can be good so that it is good enough to block DC and good enough to pass audio at maybe 20 Hz so the transition band is sharp enough with small amount of processing power.
Why a filter uses double precision arithmetic instead of single precision depends on what kind of filter it is, FIR, IIR, biquad, etc. Some constructs like biquads are very useful but need careful handling not to become unstable due to coefficient truncation etc. And another thing to remember is that single precision floating point arithmetic only gives 23 bits of mantissa, so in some sense it's a bit worse (pun intended) than 24-bit linear PCM, and that can make a difference.
floatyou can get a theoretical 120 dB, but even 100 dB should be fine (unless you're after world records). \$\endgroup\$