Those are the codecs.
DTS Coherent Acoustics is a perceptual audio codec. The main technique used is a QMF filter together with Huffman, ADPCM and vector quantization.
White Paper: An Overview of the Coherent Acoustics Coding System
Apt-X100 is a proprietary codec, hence why you can't very information about it. CSR the company that developed and licenses aptX are not that liberal with the detailed inner workings.
You can find some insight in this excerpt, but leads to more extensive reading.
DTS: BRIEF HISTORY AND TECHNICAL OVERVIEW
If your intentions are serious about understanding the workings your best bet is to contact Dr. David Trainor at CSR and see were that takes you. Be careful on the direction you take this because technically you have to pay a licensing fee to use this proprietary codec.