Graduate Thesis Or Dissertation
 

A study of the quantization procedure : higher order information and the conditions for minimum error

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/bn999876c

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  • Quantization is a non-linear operation of converting a continuous signal into a discrete one, assuming a finite number of levels N. A study is made of the quantization procedure, starting from the year 1898 to the present time. Conditions for minimum error are derived with consideration of quantization in magnitude and time. An extension of the Mehler and Carlitz formulas involving Hermitian polynomials (quadrilinear case) has been created. Further, investigation is conducted toward obtaining an autocorrelation function of the output of the quantizer for Gaussian input. The method calls for the use of two different forms of the Euler-Maclaurin sum formulas and results are derived for a hard limiter, linear detector, clipper, and a smooth limiter. The method lends itself to the extension to the non-uniform case.
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