Hi Charles,
The ADAU1772 is not a DSP in the same sense as the ADAU1701 or other SigmaDSPs. The ADAU1772 has a small filter engine that allows up to 31 IIR filters to be executed in the span of a single sample. There are also very basic functions like phase inversion (pass the signal through an allpass filter with a linear gain of -1), addition and subtraction.
Most active noise cancellation applications are simply filters and small delays on the order of a few samples, along with phase inversion or addition/subtraction. So the ADAU1772's processing engine and algorithm library, while limited, are suited for this kind of application.
If you look in the toolbox of algorithms for the ADAU1772, you'll see algorithms like filters, addition, and volume.
