How do I update my software on my Apple TV if the television isn't supporting my ATV anymore since the last update. Can I update through iTunes?

Since I last updated ATV my own tv no longer supports my ATV. On my HDMI channel it is picking up different Hz levels ranging from 18 Hz to 180 Hz when ATV is plugged in. A few times some white lines have appeared on the screen as though it is trying to connect. I have tested a different HDMI chord and that didn't have any effect and I've reset my Wi-if router. My tv still supports my bluray DVD player through the HDMI port. I want to update my ATV as I think that will fix the problem, but I can't see the menu on the tv to do so. Is there any way I can do this via iTunes or iPad?