yer a class-D
as to filter well yer but you may not need it
I mean the machine is rated for 24Vac, it aint gonna be that high of a power, ie not much current.,
Now the thing is he is running of 12V so he either puts a 1:3 transformer in to boost the voltage up (in which case that XFMR will take out the switching freq harmonics) and switch suitable FET's at >50khz and you are gonna get a really good sinus generated and that 50khz component will not appear at the load
or he is gonna have to boost that 12V first to ~40Vdc before invertering in which case a filter will be needed