On the autocorrelation and the triple correlation equation for complex-valued signals

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.