I think the book [Engineering Applications of Noncommutative Harmonic Analysis](http://books.google.com/books/about/Engineering_Applications_of_Noncommutati.html?id=o9wArx_zIsEC) by Chirikjian and Kyatkin might be exactly what you are looking for.  Although I haven't read very much of it, the sections that I have read are very nice and seem mathematically rigorous, yet geared toward applications.