Abstract
In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the Σ∆ quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate. We build on our previous result, which extends signal decimation to finite frames up to the second order. In this study we introduce a new scheme called adapted decimation, which yields polynomial reconstruction error decay rate of arbitrary order with respect to the oversampling ratio, and exponential decay rate with respect to the bit-rate.
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