I had a 400 watt PSW inverter.
I watch a lot of Antenna TV, on my 12vdc TV
Turn on the inverter, to power something else, and a few TV stations would instantly go away. Turn inverter off and they come right back. Not weak TV stations on the cusp or reception either. Seems the channels broadcast on actual VHF hi to about 19 were worst affected. This symptom is not voltage related, it is RFI related. My 12v TV works fine at 9.5v input, perhaps less.
So if pulling in distant TV stations on an antenna, perhaps even close ones, is what you want to use the TV for, then perhaps the inverter route is not the way to go.
I am biased, I am anti inverter when there are other options. I view them as a necessary evil, to be bypassed whenever possible. but that is my opinion.