Filter design for MIMO sampling and reconstruction

We address the problem of finite impulse response (FIR) filter design for uniform multiple-input multiple-output (MIMO) sampling. This scheme encompasses Papoulis´ generalized sampling and several nonuniform sampling schemes as special cases. The input signals are modeled as either continuous-time or discrete-time multiband input signals, with different band structures. We present conditions on the channel and the sampling rate that allow perfect inversion of the channel. Additionally, we provide a stronger set of conditions under which the reconstruction filters can be chosen to have frequency responses that are continuous. We also provide conditions for the existence of FIR perfect reconstruction filters, and when such do not exist, we address the optimal approximation of the ideal filters using FIR filters and a minmax l₂ end-to-end distortion criterion. The design problem is then reduced to a standard semi-infinite linear program. An example design of FIR reconstruction filters is given.