Statistical theory of quantization

The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to floating-point quantization is demonstrated.

[1]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[2]  W. Sheppard On the Calculation of the most Probable Values of Frequency‐Constants, for Data arranged according to Equidistant Division of a Scale , 1897 .

[3]  W. R. Bennett,et al.  Spectra of quantized signals , 1948, Bell Syst. Tech. J..

[4]  William K. Linvill,et al.  Sampled-Data Control Systems Studied Through Comparison, of Sampling with Amplitude Modulation , 1951, Transactions of the American Institute of Electrical Engineers.

[5]  B. Widrow A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory , 1956 .

[6]  B. Widrow Analysis of amplitude-quantized sampled-data systems , 1961, Electrical Engineering.

[7]  B. Widrow Statistical analysis of amplitude-quantized sampled-data systems , 1961, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[8]  J. Katzenelson,et al.  Discussion of "On errors introduced by combined sampling and quantization" , 1963 .

[9]  B. Liu,et al.  Error analysis of digital filters realized with floating-point arithmetic , 1969 .

[10]  G. H. Robertson Computer study of quantizer output spectra , 1969 .

[11]  R. W. Hamming,et al.  On the distribution of numbers , 1970, Bell Syst. Tech. J..

[12]  A. Oppenheim,et al.  Effects of finite register length in digital filtering and the fast Fourier transform , 1972 .

[13]  Bede Liu,et al.  On Local Roundoff Errors in Floating-Point Arithmetic , 1973, JACM.

[14]  A. Sripad,et al.  A necessary and sufficient condition for quantization errors to be uniform and white , 1977 .

[15]  A. J. Jerri The Shannon sampling theorem—Its various extensions and applications: A tutorial review , 1977, Proceedings of the IEEE.

[16]  A. Sripad,et al.  Quantization errors in floating-point arithmetic , 1978 .

[17]  A. J. Jerri Correction to "The Shannon sampling theorem—Its various extensions and applications: A tutorial review" , 1979 .

[18]  T. Claasen,et al.  Model for the power spectral density of quantization noise , 1981 .

[19]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[20]  D. T. Sherwood Some Theorems On Quantization And An Example Using Dither , 1985, Nineteeth Asilomar Conference on Circuits, Systems and Computers, 1985..

[21]  Istvv An Kolll Ar The Noise Model of Quantization , 1986 .

[22]  IEEE standard for radix-independent floating-point arithmetic - IEEE standard 854-1987 , 1987 .

[23]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[24]  Robert M. Gray,et al.  Quantization noise spectra , 1990, IEEE Trans. Inf. Theory.

[25]  R. Marks Introduction to Shannon Sampling and Interpolation Theory , 1990 .

[26]  A. Lacroix,et al.  Distribution densities of the mantissa and exponent of floating point numbers , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[27]  John Vanderkooy,et al.  Quantization and Dither: A Theoretical Survey , 1992 .

[28]  Yrjö Neuvo,et al.  Floating-point arithmetic in signal processing , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[29]  Robert M. Gray,et al.  Dithered quantizers , 1993, IEEE Trans. Inf. Theory.

[30]  Dario Petri,et al.  Effect of additive dither on the resolution of ideal quantizers , 1994 .

[31]  István Kollár Bias of mean value and mean square value measurements based on quantized data , 1994 .

[32]  Diego Bellan,et al.  Quantization theory in electrical and electronic measurements , 1995, Proceedings of 1995 IEEE Instrumentation and Measurement Technology Conference - IMTC '95.

[33]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[34]  HE Ixtroductiont,et al.  The Bell System Technical Journal , 2022 .