Yes of course I expected to have some noise because of electrochemical reactions, but my practical experience tells me that this is the cleanest of all other types of PSUs. Whenever I connect a battery on sensitive equipment, all hum dissapear and noise goes down.
Although I have not made any practical measurements, Jean Hiraga in his battery powered amplifiers shows with measurements the lowers noise achieved by batteries. But I am not so confident.
I wonder if a well designed regulator will benefit from a battery as a psu source at all.
I have an example here **broken link removed** Where a two stage regulator is used to regulate and to clean the DC. Will this benefit from a battery source at all?
Perhaps an advise of how to measure the PSU noise will help more.