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Vector sampling expansion

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2 Author(s)
Seidner, D. ; Dept. of Electr. Eng. Syst., Tel Aviv Univ., Israel ; Feder, M.

The vector sampling expansion (VSE) is an extension of Papoulis' (1977) generalized sampling expansion (GSE) to the vector case. In VSE, N bandlimited signals, all with the same bandwidth B, are passed through a multi-input-multi-output (MIMO) linear time invariant system that generates M (M⩾N) output signals. The goal is to reconstruct the input signals from the samples of the output signals at a total sampling rate of N times the Nyquist rate, where the Nyquist rate is B/π samples per second. We find necessary and sufficient conditions for this reconstruction. A surprising necessary condition for the case where all output signals are uniformly sampled at the same rate (N/M times the Nyquist rate) is that the expansion factor M/N must be an integer. This condition is no longer necessary when each output signal is sampled at a different rate or sampled nonuniformly. This work also includes a noise sensitivity analysis of VSE systems. We define the noise amplification factor, which allows a quantitative comparison between VSE systems, and determine the optimal VSE systems

Published in:

Signal Processing, IEEE Transactions on  (Volume:48 ,  Issue: 5 )