Minimum Mean Square Error Quantizer
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Reddit Request full-text A Simple Approximation for Minimum Mean-Square Error Symmetric Uniform QuantizationArticle in IEEE Transactions on Communications 32(4):470 - 474 · May 1984 with 30 ReadsDOI: 10.1109/TCOM.1984.1096081 · Source: IEEE Xplore1st Fu-Sheng Lu2nd Gary L. WiseAbstractIn the quantization of signals context of minimum mean-square error symmetric uniform quantization, we show that for several
Quantization Error
different distributions on the input signals, log-log plots of step size versus number of output levels and mean-square error versus what is quantization number of output levels both exhibit nearly linear behavior. This observation results in a straightforward design procedure for symmetric uniform quantization.Do you want to read the rest of this article?Request full-text CitationsCitations5ReferencesReferences3Asymptotic analysis of
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optimal fixed-rate uniform scalar quantization"Apart from these, there exists an oft cited rule of thumb [c.f. 12, p. 125] for choosing ∆ to be approximately 4σ / N , where σ is the standard deviation of the source, but this applies only to a very limited range of N 's. In studying the results of numerical algorithms, some researchers [13, 14] noticed the near linearity of the quantization error formula log-log plots of ∆ N and D N versus N for some common source densities such as Laplacian, Gaussian, Gamma and Rayleigh. Accordingly, they proposed simple approximations of the form of a N − b , where a and b are positive constants chosen to fit the numerically computed values of ∆ N and D N . "[Show abstract] [Hide abstract] ABSTRACT: Studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean-squared error (MSE). When a symmetric source density with infinite support is sufficiently well behaved, the optimal step size ΔN for symmetric uniform scalar quantization decreases as 2σN-1V¯ -1(1/6N2), where N is the number of quantization levels, σ2 is the source variance and V¯-1 (·) is the inverse of V¯(y)=y-1 ∫y ∞ P(σ-1X>x) dx. Equivalently, the optimal support length NΔN increases as 2σV¯-1(1/6N2). Granular distortion is asymptotically well approximated by ΔN2/12, and the ratio of overload to granular distortion converges to a function of the limit τ≡limy→∞y-1E[X|X>y], provided, as usually happens, that Ï„ exists. When it does, its value is related to the number of finite moments of the source density, an asymptotic formula for the overall distortion DN is obtained, and Ï
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