Performance of Sigma-Delta quantizers in the context of oversampled filter banks

We consider the computation of the MSE for the first-order Sigma-Delta (SD) quantizers in the context of an oversampled Filter Bank (FB). We use the same SD quantizer model than the one used by Benedetto et al.(2004), we establish that the reconstruction minimum squares error (MSE) behaves as _r ^1/2 where r denotes the frame redundancy. This result is shown to be true both under the quantization model used in Benedetto et al.(2004) as well as under the widely used additive white quantization noise assumption.