  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 $\Sigma\Delta$ quantization scheme,
the reconstruction error decays exponentially with respect to the bit-rate. In
this study, similar results have been proven for finite unitarily generated
frames. We have devised a process called alternative decimation on finite
frames that is compatible with $\Sigma\Delta$ quantization up to the second
order. In both cases, decimation results in exponential error decay with
respect to the bit usage.
