In the design of pseudonoise generators with user-specified characteristics it is possible for the user to inadvertently specify incompatible combinations of probability density function (PDF) and power spectral density. A method is presented which harnesses evolution procedures for optimizing the characteristics of the achieved power spectrum by windowing the corresponding autocorrelation function, given a particular target PDF. It is shown that for a given PDF (truncated Cauchy) it is possible, by appropriately costing spectral negativity infractions, to produce a positive approximation to the specified power spectrum. >

http://ieeexplore.ieee.org/iel5/555/4470/00176101.pdf

Windowing to simultaneously achieve arbitrary autocorrelation characteristics and probability densities in noise generators

The authors show that, despite their recursive nature, linear congruential pseudorandom number generators may be pipelined for high speed operation by means of the Messerschmitt transformation using an iterated version of the system equation. They suggest an appropriate architecture for multiply iterated LCGs pipelined in this way: the hardware overhead required to obtain high speed operation by means of this technique, mainly connected with a more complicated initialisation procedure, is judged to be acceptable. The technique is illustrated by determining the system parameters for multiply iterated versions of the high performance Wichmann-Hill algorithm. Work is in hand to optimise the implementation for VLSI.

Fast linear congruential pseudorandom number generators using the Messerschmitt pipelining transformation

Bibliography on higher-order statistics

In the design of a nonlinear filtering system to generate a random process, z(t), with specified probability density function, pz(·), and specified power spectral density, Wz(f), some combinations of pz(·) and Wz(f) lead to violation of the positivity property of the power spectrum of the filter output. Three numerical spectral conditioning techniques (multiple windowing of the autocorrelation function, ‘partial-raising/ partial-lowering’ of the power spectrum and a combination of both) for finding minimum normalised mean squared error positive approximations to the required spectrum are described.

Correlation windowing and spectral biasing in the design of noise generators having specified probability densities and power spectra

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Correlation windowing and spectral biasing in the design of noise generators having specified probability densities and power spectra

Windowing to simultaneously achieve arbitrary autocorrelation characteristics and probability densities in noise generators