A two channel approach for system approximation with general measurement functionals

The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. However, the convergence of the approximation series is not guaranteed: there exist stable LTI systems and bandlimited input signals such that the approximation series diverges, regardless of the oversampling factor and the sampling pattern. Recently, it has been shown that this divergence can be overcome by using measurement functionals instead of pointwise sampling. However, the bandwidth of the approximation series needs to be strictly larger than the signal bandwidth. In this paper we derive a two channel system approximation approach based on measurement functionals that converges for all stable LTI systems and all signals in the Paley-Wiener space PW
_π
¹
. Thanks to the two channel structure it is possible to achieve an approximation bandwidth that is equal to the signal bandwidth.