Introduction (Vaseghi - Advanced Digital Signal Processing and Noise Reduction), страница 5
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The quantisation noise is defined ase( m )= x ( m ) − xa ( m )(1.26)Now consider an n-bit quantiser with an amplitude range of ±V volts. Thequantisation step size is ∆=2V/2n. Assuming that the quantisation noise is azero-mean uniform process with an amplitude range of ±∆/2 we can expressthe noise power as26Introduction[û/ 2]û/ 21E e (m) = ∫ f E (e(m) ) e (m) de(m) = ∫ e 2 (m) de(m)û −û/ 2−û / 22=22(1.27)2 − 2nû V 2=123where f E (e(m)) = 1/ ∆ is the uniform probability density function of thenoise. Using Equation (1.27) he signal–to–quantisation noise ratio is givenby E [ x 2 (m)] P =10 log10 Signal SQNR (n) =10 log10 22 −2nV 2 /3 E [e (m)] V2 + 10 log10 22 n= 10 log10 3 −10 log10 PSignal = 4.77 − α + 6 n(1.28)where Psignal is the mean signal power, and α is the ratio in decibels of thepeak signal power V2 to the mean signal power Psignal.
Therefore, fromEquation (1.28) every additional bit in an analog to digital converter resultsin 6 dB improvement in signal–to–quantisation noise ratio.Continuous–amplitude samplesx(mT)Discrete–amplitude samples+V+2∆11+∆1002V01−∆00−2∆−VFigure 1.21 Offset-binary scalar quantisationBibliography27BibliographyALEXANDER S.T. (1986) Adaptive Signal Processing Theory andApplications. Springer-Verlag, New York.DAVENPORT W.B.
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