A headphone amp that connects to ipod touch through sync connection instead of headphone output

what you are looking for is an LOD

http://www.amazon.com/FiiO-L3-Line-Cable-iPhone/dp/B003UCESP8/ref=pd_cp_e_1

What you are looking at is the Cypher Labs Algorhythm Solo (http://www.cypherlabs.com/product) or the Fostex HP-P1 (http://www.fostexinternational.com/docs/products/HP-P1.shtml)

The former does not have a built in headphone amp but the latter does. Both are pretty expensive, CLAS is about $570 while the Fostex is about $640.

If you don't need it to be portable there is a pretty cheap Ipod dock, the i-20 dock with more connections than you need: http://www.pure.com/products/product.asp?Product=VL-61429

I have not heard all of them. Personally, I am moving away from investing too much money into portable audio, instead I am trying to build a desktop system.

Guys, I think we should explain to OP that there's a difference between analogue and digital signals here.

OP, you can either extract an analogue signal (bypass the amp), or a digital signal (bypass DAC and amp) from the "sync connection" of an iPod. That connection is commonly known as the Line-Out Dock, or LOD.

To hook up an amp, you will need a LOD cable. There are many options for cables, and some can be quite cheap (as alv4426 pointed out). This extracts an analogue signal. You can hook up any amp with any of these cables.

To hook up a DAC or DAC+amp, you will need to choose from a few, more expensive, specially-licensed products. This is what koonhua90 is referring to. I think the cables packaged with these products are different from the cheaper LOD cables you can buy for an analogue signal.

By the way, you can't listen to digital signal, well, not like you can't, it will sound like random high frequency noise. 

In a strict sense, there is no real digital signal (except maybe in the realm of quantum computing) that is discrete in time and discrete in amplitude. The digital signal that we talk about is actually discrete in time and continuous in amplitude. This is because there is no zero time charging. You can not get any work done in zero time, because you can't charge a capacitor in zero time, and this is just physics.

Fully analog signal is continuous in time and continuous in amplitude. 

In Ipod, you have DAC (digital to analog converter) that converts the 1s and 0s to your analog music signal. You can use a line out cable to extract the analog music signal (which is processed by the internal Ipod DAC) to feed it into an external amplifier. Some people who are more hardcore and want more would use an external DAC, and only two portable devices right now can bypass the internal DAC of Ipod and use the external DAC to process the bits. There should be some amps/DAC combo that accept SPDIF input, but I am not sure.

Some good cheap amps would be the Fiio amps, although I have not heard them, my friend said they are pretty good for the price. Just don't expect the amp to make your earphone/headphones sounds 2x better.

edit: 2 seconds of googling made me feel stupid.