On the construction of a random process with given power spectrum and probability density function

Often random processes with a given probability density function (pdf) and a given power spectrum are desired. Usually a discrete-time linear system is used to shape the power spectrum of an i.i.d. excitation process in the desired manner but there does not exist a solution to simultaneously adjust...

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Bibliographic Details
Published in:Circuits and Systems; Proceedings: Midwest Symposium on Circuits and Systems pp. 14 - 17
Main Authors: Letsch, K., Matzner, R.
Format: Conference Proceeding
Language:English
Published: IEEE 1998
Subjects:
Electrical capacitance tomography
Electronic switching systems
Identity-based encryption
Linear systems
Noise shaping
Nonlinear filters
Polynomials
Power engineering and energy
Probability density function
Random processes
ISBN:9780818689147, 0818689145
Online Access:Get full text
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Summary:Often random processes with a given probability density function (pdf) and a given power spectrum are desired. Usually a discrete-time linear system is used to shape the power spectrum of an i.i.d. excitation process in the desired manner but there does not exist a solution to simultaneously adjust the output pdf. In this paper a method is introduced to adjust the pdf at the output of a given linear system to almost any desired shape by computing the required pdf of the excitation process, which can easily be shaped by a memoryless nonlinear system without any impact on the power spectrum. The method is based on Hermite polynomials to obtain an approximation of the pdf, cumulants to describe the effect of the linear system on the pdf, and a combinatorial algorithm to complete the Hermitian coefficients from cumulants, and vice versa. A numerical example gives evidence of the practical applicability.
ISBN:9780818689147
0818689145
DOI:10.1109/MWSCAS.1998.759424