Analog filter banks for sampling: Discretization, polyphase form, and role in compressive sensing

Continuous-time signals arising in many applications can often be modeled as the outputs of analog synthesis-filter banks driven by discrete-time inputs d_i(n). Such a signal x(t) has a finite innovations rate, although it may not be bandlimited in general. In some applications it is necessary to sample such signals after filtering with an analog sampling-filter-bank, to recover the driving signals d_i(n): This sampling filter bank is in general not unique, and the theory and design techniques for such analog filter banks are not as well developed as the large body of literature on digital filter banks. In this paper we show that the theoretical as well as design and implementation issues can be formulated in terms of digital filter banks, by taking advantage of the finite innovations rate of x(t): The rich body of knowledge on digital filter banks and polyphase forms can therefore be utilized and furthermore the optimization of the sampling filter bank can be done on a more convenient platform. Applications of this development in the context of compressive sensing are also elaborated.