This is a version of a wooden typeface created by William Hamilton Page in the 19th century and now known as Concave Tuscan extra condensed bold with side spurs. Wooden Type Fonts has done a digital recreation of the font, without side spurs:
http://www.myfonts.com/fonts/woodentypefonts/concave-tuscan-x/condensed-...

Thought also to some Concave Tuscan but gave up with the idea, too much different for me (/M centre vertex, median side spurs/thorns, slab...). Here are some I collected during the search: Boxwood, Winnetka JNL, Antique Tuscan Condensed ID, Antique Tuscan Condensed WTF, Council
Don't know why but reminds me also some 'Tiki' fonts... and Totally Gothic...

Thanks Ryuk for the collection of Concave Tuscan & Antique Tuscan variations, particularly the ones like, Boxwood, WinnetkaJNL and CouncilEM which so not show up in Tuscan searches.
Don

I was going to do a mockup of the words TAEKWONDO but found that it is too much of a Frankenfont to make this easy. Some letters have a base design, i.e. excluding the horizontal spurs which can be pasted on, that resemble Concave Tuscan: T, A, K, W [if apex brought to a point], O and N. Others have a base design, again excluding the spurs, that uses slab serifs: E and D. This is almost certainly not a revival of any classic font that I have seen.
Perhaps it might be most effective to ask the embroidery company about its source for the letters.
Don

duplicate
Don

To test the match of Concave Tuscan Extra Condensed by Wooden Type Fonts, I used it to as a base for the letters TA K ONDO, added spurs and did some relatively minor tinkering with the outlines. I made D by adding serifs to O.

Great job, Don! Just found Becker Gothics Concave DTF, the closest so far to me. Adding slab serifs on /D, reworking /W centre vertex and scaling it horizontally should do the job quite nicely.