Adapted Decimation on Finite Frames for Arbitrary Orders of Sigma-Delta Quantization

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 ΣΔ 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.