How to filter the stepped wave from inverter?
I fear that your inverter is a square wave type which may have been marketed as a "modified sine wave" .It is feasible to filter the output .The filter components have to have meaningful reactance at 150Hz or 180Hz .This is the third harmonic of mains 50 or 60Hz .Given that you have the invertor and dont want to buy a more expensive sine wave model then you can add inductance in series with the loads that are buzzing.Speaking from experience a 40watt 4ft flouro ballast choke is good .It can handle up to about half an amp .This should turn the nasty buzz into a nice soft hum on your ceiling fan .So summing up lamp ballast chokes can be effective and should be tried if you can lay your hands on some.