Derivation of Asymptotic Formulas for the Signal-to-Noise Ratio of Mismatched Optimal Laplacian Quantizers 


Vol. 33,  No. 5, pp. 413-421, May  2008


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  Abstract

The paper derives asymptotic formulas for the MSE distortion and the signal-to-noise ratio of a mismatched fixed-rate minimum MSE Laplacian quantizer. These closed-form formulas are expressed in terms of the number Ν of quantization points, the mean displacement μ, and the ratio ρ of the standard deviation of the source to that for which the quantizer is optimally designed. Numerical results show that the principal formula is accurate in that, for rate R=?₂Ν≥6, it predicts signal-to-noise ratios within 1% of the true values for a wide range of μ and ρ. The new findings herein include the fact that, for heavy variance mismatch of ρ＞3/2, the signal-to-noise ratio increases at the rate of g/p ㏈/bit, which is slower than the usual 6 ㏈/bit, and the fact that an optimal uniform quantizer, though optimally designed, is slightly more than critically mismatched to the source. It is also found that signal-to-noise ratio loss due to μ is moderate. The derived formulas can be useful in quantization of speech or music signals, which are modeled well as Laplacian sources and have changing short-term variances.

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  Cite this article

[IEEE Style]

S. Na, "Derivation of Asymptotic Formulas for the Signal-to-Noise Ratio of Mismatched Optimal Laplacian Quantizers," The Journal of Korean Institute of Communications and Information Sciences, vol. 33, no. 5, pp. 413-421, 2008. DOI: .

[ACM Style]

Sangsin Na. 2008. Derivation of Asymptotic Formulas for the Signal-to-Noise Ratio of Mismatched Optimal Laplacian Quantizers. The Journal of Korean Institute of Communications and Information Sciences, 33, 5, (2008), 413-421. DOI: .

[KICS Style]

Sangsin Na, "Derivation of Asymptotic Formulas for the Signal-to-Noise Ratio of Mismatched Optimal Laplacian Quantizers," The Journal of Korean Institute of Communications and Information Sciences, vol. 33, no. 5, pp. 413-421, 5. 2008.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880