Spectra of Quantized Signals

On quantization of finite frame expansions: sigma-delta schemes of arbitrary order

“…• WNH asymptotically true as size of alphabet increases [ 4,16,17 ] Works well with large alphabets! 3.2.…”

“…Recently frames have been used to describe analog-to-digital (AD) conversion and specifically the quantization algorithm known as Σ∆. While there are numerous papers on Σ∆ in the engineering literature, [4,8,10,11,15,19,20] to which this list does not begin to do justice, a paper of Daubechies and DeVore [9] created great interest in the mathematical community [12][13][14]17,21]. In particular, Benedetto, Powell and Yilmaz [1,2] recently used finite frames to describe and examine first order Σ∆ schemes, followed by Bodmann and Paulsen [6].…”

Chatting in distributed quantization networks

“…where ≃ indicates that the ratio of the two expressions approaches 1 as K increases [19], [20]. Hence, the MSE performance of a scalar quantizer can be approximated by a simple relationship between the source distribution, point density and codebook size, and this relation becomes more precise with increasing K. Moreover, quantizers designed according to this approximation are asymptotically optimal, meaning that the quantizer optimized over λ has distortion that approaches the performance of the best Q K found by any means [21]- [23].…”

Adaptive quantization using piecewise companding and scaling for Gaussian mixture

“…By using Bennettt's [35] approximate expression for the mean square distortion for very large number N of quantizer output levels, we have:…”