AC condition

It sounds like the compressor in your A/C unit may be having a problem starting. This can happen more often as the voltage supply drops. It causes the compressor to load down your electrical for a longer time. Call an A/C company and have them install an item called a hard start kit. I helps your compressor start faster and cause less of a load on your electrical service at startup. They are also easy to install if you are mech. inclined. This may not fix your issue entirely but may shorten the effect. I put this item on any units I work on.
Also when was the last time you had the electrical connections tightened on your service?

TV picture breakup or sudden shrinkage when an AC compressor kicks in is a symptom of sudden severe voltage drop. It is not RFI related. Hevac1's suggestion is good, although I think some assumptions are being made in this thread. What size is the air conditioner ? What is the condition of the household electrical service ? A small window air conditioner on the same 120V leg, with old, inadequate wiring can create similar symptoms.

I am assuming you have central A/C. If this is also a large window A/C over 12000 BTU this will still be cost effective. If it is cause by a small window unit, buy a new one.
I suggest you have your electical check to see if the breaker teminals, outlets for window unit or disconnect at your central A/C connections are loose.
This can also save you money as loose connections cause wires to heat up and draw more current.
I tighten my electrical connections every two years or so, especially on large appliance feeds and my sound room.

Run a dedicated line to your electronics and make sure the AC is on the other side of the panel from the dedicated line.

If you can't run a dedicated line, then have an electrician move your audio line to the other side of the panel, isolating it from the AC line.

Perhaps if an old home, you may need to update the panel or you could add on a poney panel and isolate some lines.

Make sure the wiring in the walls meets code,they can get pretty hot if they aren't the proper guage and AC is drawing a lot of juice.

Old homes have been known to lack the proper guage wiring for all of todays conveniences.

Assumption is not the solution to the problem as in such cases you need you consult with a professional ac repair who can check in it why this problem has been occurred . This might be the voltage drop problem because they both are in the same outlet. So in such problem having the professional advice is really helpful.