The filaments will run off either AC or DC because they're basically just heaters. AC became the norm in mains-powered devices after electrification took off, but a lot of the early radios were powered by DC from batteries - initially this was seperate, possibly rechargable, low voltage battery for the filament supply and a disposable high-voltage battery, with the second battery being replaced by step-up devices using vibrators and transformers fairly early on.