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On the autocorrelation and the triple correlation equation for complex‐valued signals
Author(s) -
v. Wolfersdorf L.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310079
Subject(s) - mathematics , autocorrelation , mathematical analysis , fourier transform , continuation , cauchy's integral formula , holomorphic function , complex plane , cauchy distribution , transformation (genetics) , initial value problem , cauchy problem , statistics , biochemistry , computer science , gene , programming language , chemistry
The paper deals with the autocorrelation equation on a finite interval and on the half‐axis and with the triple correlation equation in the case of complex‐valued signals. Via methods of Fourier transformation the equations are reduced to boundary value and continuation problems for holomorphic functions in the upper half‐plane and to functional equations in two independent variables, respectively, and in this way solved in closed form. Thereby, on the one side, Cauchy integrals and Paley‐Wiener conditions and, on the other side, the solution of a known functional equation in a single variable are applied.