Asymptotic Analysis of Optimal Uniform Polar Quantization

Multiproduct Uniform Polar Quantizer

“…However, the analysis of UUPQ presented in [13] and [14] was incomplete and not quite correct from the following reasons: in [13] the overload distortion was neglected and the optimization of r max was not done (instead of that, the value of r max for the scalar uniform quantizer was used); in [14] the expression for the overload distortion was not given and the method for calculation of r max was not explained. Due to these reasons, performances of UUPQ calculated using the analysis from [13], [14] is not accurate enough.…”

“…We will recall some results from [13], [14]. The expression for the number of magnitude levels was derived in [14]:…”

“…In [13], the following expression for the number of phase levels on the i-th magnitude level was presented: …”

“…The asymptotic analysis is usually used for the designing of polar quantizers [3][4][5][6][7][8][9][10][11][12][13][14]. Hence, the asymptotic analysis will be applied in this paper.…”

“…It was analyzed in [13], [14]. It is two-dimensional polar counterpart of the scalar uniform quantizer.…”