PCM distortion analysis

Quantization errors of modulo sigma-delta modulated ARMA processes

“…In a recent report [9], we proved that the conclusion also holds for a fGn process with the Hurst exponent H ∈ (0, 1 2 ). Such a fGn process can also be viewed as a special causal staThis work is supported in part by National Natural Science Foundation of China 61021063 and National High-Tech Research and Development (863) Program of China 2012AA112305.…”

“…The use of high resolution theory for quantization error analysis dates back to late 1940s [1]- [2]. In [2], Bennett demonstrated that under the assumption of high resolution and smooth density of the sampled stochastic process, the quantization error can be treated as an additive white noise.…”

On the Spectral Tones in a Digital-Analog Converter Due to Mismatch and Flicker Noise

“…The approach to computing the individual current source spectrum is inspired from the original classic development on quantization noise spectrum by Clavier, Panter, and Grieg [4], [5], and subsequent treatment by Gray [6]. In this work, a Fourier series expansion of the quantization error sequence was obtained as a function of the input signal .…”

Bounds on performance of optimum quantizers

“…As Smith [2] notes, Sheppard [101 was the first to give the effect of a uniform quantizer (i.e., grouping statistical data in uniform intervals) on variance in 1898. Sheppard's correction, missed by Clavier et al [11] in the first paper on PCM distortion, is rederived by Bennett [12] and by Oliver et al [13]. Smith gives later statistical references on uniform quantization; Cox [14], in 1957, writes on optimum spacing of K -1 levels to minimize the meansquare error in grouping normally distributed data into K intervals, and designs an optimum K-interval quantizer in the mean-square difference sense for K = 2 to K = 6 for the Gaussian distribution by numerical calculation, not referenced by and not referencing the communications literature and missing (2).…”