What Filter Banks have to do with Ergodic Theory

I will explain how stable signal recovery from the output of an iterated down-converting filter pair and the theory of the associated Schauder basis (frames) in l^2 connects with the Perron-Frobenius operator and cohomology of multiplicative cocycles, as known from the theory of iterated maps. This will be an elementary introduction but we will try to delve into "how-the-sausage-is-made" technicalities.