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   -> Volume 11, Issue 1


Preprint: On simple oversampled A/D conversion in shift invariant spaces
 
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Wen Chen (wenchen@math.ualberta.ca)
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PostPosted: Tue Apr 09, 2002 5:02 pm    
Subject: Preprint: On simple oversampled A/D conversion in shift invariant spaces
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Recently we finished a new manuscript which is available by sending email to
wenchen@math.ualberta.ca (Wen Chen) --- Wen

Title: On simple oversampled A/D conversion in shift invariant spaces

Abstract:
In this paper we study a simple oversampled analog-to-digital (A/D) conversion in shift invariant spaces. The Beurling-Landau type theorem for bandlimited signal spaces is extended to shift invariant spaces, and then a non-uniform sampling theorem for shift invariant spaces is established, which says, a uniformly discrete set is a stable sampling set for a shift invariant space if its Beurling lower density is larger than a fixed density determined by the generator of the shift invariant space. Consequently, an oversampling theorem for shift invariant spaces is attained. These sampling theorems together with a theorem concerning the stability of stable sampling in shift invariant spaces shown by us, are used to build a simple oversampled A/D conversion scheme in shift invariant spaces. In such scheme, the quantization error $e$ is found to behave as $\|e\|^2 = O(greek_tau.gif^2)$ with respect to the sampling interval $greek_tau.gif$, which is the same as that for bandlimited signal spaces derived very recently. Moreover, we demonstrate that the bit-rate required to encode the converted digital signal only increases as logarithm of sampling ratio.
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