Can I Connect to TV with HDMI to DVI cable and optical audio

Your TV would need to support HDCP and 720p, even then it isn't guaranteed that it will work with DVI, the Apple TV specifications state an HDMI enabled TV is required.

Assuming your TV supports HDCP and 720p, of course it should work, Winston's standard FUD notwithstanding, not to mention his repeated failures to acknowledge Apple documentation that refers to using DVI with the ATV. It goes without saying that it should work, which is perhaps why "the specifications" omit it. They don't mention you can use an electrical extension cord, either.

HDMI is not the same as DVI without audio, nor is it an extension lead for HDMI, there has been reference to DVI in one kb document but not in any others or in the specifications. DVI can pass video from HDMI assuming none of the standards that apply to HDMI and not to DVI are in use.

I draw inference from the fact that Jon always uses the word should and not will, perhaps he is mindful of a number of users who claim to have HDCP/720p compliant TV's yet are unable to get their Apple TV's to work over DVI. I know I do, which is why I continue to state there is no guarantee.

Winston, if Apple support articles that refute your repeated wrong statements aren't sufficient, I've previously referred you to the HDMI.org FAQ which also refutes you. Here is the relevant excerpt:

http://www.hdmi.org/learningcenter/faq.aspx#31

Q. Is HDMI backward compatible with DVI (Digital Visual Interface)?

Yes, HDMI is fully backward compatible with DVI compliant devices. HDMI DTVs will display video received from existing DVI-equipped products, and DVI-equipped TVs will display video from HDMI sources...Also, consumers may want to confirm that the DVI interface supports High-bandwidth Digital Content Protection (HDCP), as content that requires HDCP copy protection will require that both the HDMI and DVI devices support HDCP to properly view the video content.

Which is what I've been saying. (Along with the 720p requirement.)

As for my use of the word "should", you've "inferred" wrongly about that, too. It has nothing to do with HDMI vs. DVI. It has everything to do with HDMI being such a finicky technology, and the ATV being a finicky example of the finicky. For example, lots of people have been reporting (and I can confirm) the ATV doesn't work when plugged into the HDMI ports of a variety of Denon receivers, with the Denon then being connected to a TV or monitor that does work when the ATV is directly plugged into them. Thus, it would not be a great shock to find a TV with which the ATV is incompatible using HDMI. It's got nothing to do with the use of DVI, which can be expected to work if it's there (and HDCP and 720p are supported), irrespective of the "Apple specifications" failing to mention that which goes without saying, much like they fail to mention the Apple TV is compatible with electrical extension cords, an analogy that has just failed to penetrate after multiple attempts. As I've patiently explained to you before (and this is just one of quite a few attempts to explain the technology to you and point you to additional sources):

https://discussions.apple.com/thread/3546954?answerId=16923098022#16923098022

For our purposes, a DVI cable (like the $3 one I mentioned) is an HDMI cable that doesn't carry audio. It carries video, and it will work assuming there are no HDMI handshaking issues, HDCP issues, etc. Like I said. Like Apple support articles say. Like the hdmi.org FAQ says. It's the way the technology works. When it doesn't work, it's one of the aforementioned issues, a bug, or user error, such as connecting to a monitor that doesn't support the necessary resolutions or timings (TV vs PC) . It can be expected to work. As I wrote a week or two ago, I was no more surprised it worked with my HDCP-compliant NEC monitor that supports 720p and the optical out connected to my Denon receiver than I was that the ATV worked when plugged into my UPS. It would be real news if some manufacturer released an HDMI device that didn't work over DVI. Stop trying to spread FUD about this!

You're mixing up cables and standards. A DVI cable may well be able to replace an HDMI without the audio, but a DVI display cannot necessarily replace an HDMI display, although as you say HDMI display can replace a DVI display. HDMI has features that DVI simply doesn't have.

To Winston, who always has something to say: Despite being directly refuted in multiple ways yet again, as is your usual, you haven't learned anything. Instead, you've doubled down on making silly, irrelevant statements that further betray your lack of understanding of what's being discussed. Sadly, I expect you will only continue this.

With absolute certainty I will continue, I see no good reason to tell everyone that DVI TVs will work with the Apple TV when clearly in some cases they do not, I'm happy to say they might, but it's misleading to say they will. HDMI is not DVI without audio, backwards comparability is not forwards compatibility. I think the Apple TV is the best gadget we have in our household, but I'm not about to start telling people it will do things it might not.

To Winston, who always has something to say: You will continue to spread FUD as long as you refuse to learn about the things you're offering advice on. And I responded to your "might not work" tack before:

https://discussions.apple.com/thread/3569250?answerId=17001873022#17001873022

If you're going to continue to spread FUD about DVI not working when the requirements I mentioned are met, and you're going to continue to ignore Apple support articles that say DVI is supported, you ought to at least note that HDMI doesn't always work, and for the same reason, handshaking issues. It's only fair.

Besides rejecting the Apple support articles, you've also repeatedly rejected a statement that clearly contradicts you in the hdmi.org FAQ. It is what you do.

I may have been too restrictive when I limited it to one reason in my cited post, but the point is, if you have a device with a DVI input that supports 720p and HDCP, it can be expected to work with the ATV every bit as much as a device that has an HDMI input. It's the nature of the technology and is confirmed in the hdmi.org FAQ and Apple support articles that you've repeatedly rejected. As for HDMI inputs, the ATV certainly doesn't work with all of them; see reference to Denon receivers above, which IME work fine with other devices like Roku, BD players, cable boxes, etc. I would expect the ATV has issues with other HDMI-equipped devices as well, but as I have a Denon receiver, that's the one that sticks in my mind as I see others report problems with various Denon receivers. So if you're going to spread FUD about DVI, the principles of honesty and consistency dictate that you need to spread FUD about HDMI, too. Actually, if you were to equate HDMI and DVI with the possibility of the ATV working or not working, instead of repeatedly misrespresenting DVI as some sort of red-headed stepchild, you would be speaking accurately for a change. Will you begin to speak accurately?

Thanks for the help both WC and jon

To anyone like myself who found myself here after searching for help with the same issue,

I personally find jon8979 incorrect in stating that Winston had "doubled down on making silly, irrelevant statements that further betray your lack of understanding of what's being discussed" as the original question was about both the TV and cable connection, and I know that it is best to consider each part, which is exactly as Winston has approached his explainations. Please consider what Winston had to say in this topic as much as jon8979 if you are still looking for help.