Mixed H^2/H^∞ optimal signal reconstruction in noisy filter banks

We study the design of synthesis filters in noisy filter bank systems using an H^∞ estimation point of view. The H^∞ approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank are unknown, or are too difficult to model and analyze. For arbitrary analysis polyphase matrices, standard state-space H∞ techniques can be employed to obtain numerical solutions. When the synthesis filters are restricted to being FIR, as is often the case in practice, the design can be cast as a finite-dimensional semi-definite program. In this case, we can effectively exploit the inherent non-uniqueness of the H∞ solution to optimize for an additional average performance and thus obtain mixed H^2/H^∞ optimal FIR synthesis filters.