Performance of sigma-delta quantizers in oversampled odd-stacked CMFB systems

Abstract

In this paper, we investigate the performance of the joint use of odd-stacked cosine modulated filter banks (CMFBs) and the first- and second-order Sigma-Delta (ΣΔ) quantization for communication systems when the signal expansion frame is infinite. This performance is evaluated in terms of the decrease of the reconstruction error of the signal that is jointly represented through the CMFBs and the ΣΔ quantization schemes. To begin with, we derive closed-form expressions of upper-bounds on the signal reconstruction minimum square error (MSE) for both first- and second-order ΣΔ quantization cases. Such upper-bounds are derived irrespectively of any quantization noise assumption that could be made in the considered ΣΔ quantization scheme. Exploiting the obtained upper bound closed-form expressions, we demonstrate that under a set of conditions, this signal reconstruction MSE decays as $\frac {1}{r^{2}} $ where r denotes the redundancy of the signal expansion frame. The obtained results are shown to be true under the widely used additive white quantization noise assumption, where we determine also explicit analytical signal reconstruction MSE expressions when the CMFBs are combined with first- and second-order quantizers. Simulation results are given to support our claims.