# Easing towards stepped value

I'm currently developing this rhythm game in lua (on top of a c++ engine) and I'm having trouble keeping a steady playhead position for the song currently playing.

The playhead position that the engine gives me updates in steps, so I get a fresh one every 2, 3 or 4 frames. But I need to have a steady one for sprites moving smoothly with the rhythm and stuff.

So I just keep track of my own playhead variable, which I initialize in 0 and then constantly add delta time to it. This variable eventually gets out of sync with the actual playhead, so every time I get a fresh playhead (or a "new step"), I correct my variable using the average between these two.

This however results in choppy movement.

I've seen many easing functions out there but I'm not sure which one would work in this case, nor when should I call it.

What would be the best way to ease my playhead variable into the stepped one?

This is the code I excecute every frame:

playhead = playhead + delta_time

if stepped_playhead ~= last_stepped_playhead then