Vacuum tubes heaters supply, AC or DC?
There are two types of heaters.  In one, the cathode is a hollow cylinder and the heater is inside the cathode but electrically isolated from it and everything else.  In the other type, the cathode is a wire with at least two connections.  Current is passed thru this wire to heat it while its common mode voltage is driven with whatever signal is supposed to be on the cathode.

In the first type, the heater can be driven by AC or DC.  It doesn't matter as long as the RMS voltage is right.  Common voltages were 6.3 V and 12.6 V.  This type has the advantage that since the heater is completely isolated from everything else, it can be driven directly be a separate secondary of the power transformer just for that purpose.  The downside is that it takes more power to keep the cathode at the proper temperature.

The second type must be run from well-filtered DC.  Since the cathode has some resistance end to end (it must to dissipate power), there will be a voltage difference end to end proportional to the heater current.  This will show up in the output signal if it varies.  This type of tube was usually used where power usage mattered, like in battery operated equipment.  Usually there would be a separate battery for heating the cathodes.  The heater voltage was often 3 VDC in these tubes, since that was two ordinary cells in series.