Title :
A two channel approach for system approximation with general measurement functionals
Author :
Monich, Ullrich J. ; Boche, Holger
Author_Institution :
Res. Lab. of Electron., Massachusetts Inst. of Technol., Cambridge, MA, USA
Abstract :
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 PWπ1. Thanks to the two channel structure it is possible to achieve an approximation bandwidth that is equal to the signal bandwidth.
Keywords :
approximation theory; bandlimited signals; convergence of numerical methods; linear systems; series (mathematics); signal sampling; Paley-Wiener space; approximation bandwidth; bandlimited input signal; convergence; divergence; general measurement functional; linear time-invariant systems; oversampling factor; sampling pattern; sampling series; signal processing; stable LTI systems; two channel system approximation approach; Approximation methods; Bandwidth; Convergence; Linear systems; Noise; Transforms; approximation; bandlimited signal; linear time-invariant system; measurement functional; two channel approach;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on
Conference_Location :
South Brisbane, QLD
DOI :
10.1109/ICASSP.2015.7178698