Solutions to a Filtering Problem and Convolution Equations

Autor:	G.K. Yang
Rok vydání:	1993
Předmět:	Pure mathematics Stochastic process Applied Mathematics Autocorrelation Mathematical analysis Minimization problem Spectral density Convolution symbols.namesake Fourier transform symbols Filtering problem Convolution equation Analysis Mathematics
Zdroj:	Journal of Mathematical Analysis and Applications. 176(1):108-120
ISSN:	0022-247X
DOI:	10.1006/jmaa.1993.1202
Popis:	We investigate the Tauberian minimization problem which is to characterize the criterion for achieving inf{ I ( f ): f ∈ L 1 ( R )} = I ( g ), g ∈ L 1 ( R ). The existence of "good" filters g is equivalent to the existence of solutions to certain kinds of convolution equations. Several necessary conditions are found and the criteria for the existence are characterized in terms of the power spectrum which is the Fourier transform of the observe signal. Further, all the results are extended to similar (but slightly different) problems in stochastic processes.
Databáze:	OpenAIRE
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