The Inverter needs to generate a Pure Sine wave from the "off" There is no way of moderating it afterwards at sensible money. The more money you pay for an Inverter, the better sine wave will be; so Antares and Victron will be good enough to run anything but the ones from Wun Hun Lo of Shanghai may well not be good enough.
IIRC, the fussiest item that you can put through an Ineverter is a 230vAC fridge!