Uniform Spherical Coordinate Quantization of Spherically Symmetric Sources

Multiproduct Uniform Polar Quantizer

“…4. PUPQ is well known in literature [5], [6]; this is the polar quantizer where the uniform quantization of magnitude is performed (as well as in MUPQ and UUPQ), but in PUPQ the number of phase levels is the same for all magnitude levels, i.e. P 1 = P 2 = … = P L = P. PUPQ is the simplest of those three quantizers (PUPQ, UUPQ, MUPQ) since only one parameter P has to be stored and calculated, but it has the smallest SQNR.…”

“…Polar quantization has been considered in many papers. In [3], [4] unrestricted polar quantizers were analyzed, using the optimal companding function for the quantization of the magnitude r. In [5], [6] the product uniform polar quantization was considered. The product polar quantizer with the companding function optimal for scalar but not for polar quantization, was considered in [7].…”

“…The comparison between MUPQ and PUPQ (product uniform polar quantizer) [5], [6] is also presented. It is shown that MUPQ is better solution since MUPQ is slightly more complex than PUPQ but MUPQ achieves higher SQNR compared to PUPQ.…”

“…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.…”

Optimal polar image sampling

“…This means that the two−di− mensional signal which should be quantized is circularly symmetric (it has uniform phase distribution) and its radial pdf is defined with f r ( ). Polar coordinates will be used for design of the two−di− mensional quantizer, because they are very suitable for the circularly symmetric input signal [5]. Since the phase of the two−dimensional input signal is uniformly distributed, it will be quantized with the uniform quantizer.…”