On the existence of L¹(R) solutions to wiener-Hopf type equations

Abstract

By means of the Fourier transforms of distributions we find necessary and sufficient conditions for the existence of L¹(R) solutions to Wiener-Hopf type integral equations. Thus we establish general criteria for the existence of L¹(R) filters operating on the observed signal to best approximate the true signal. The theorems apply to wide sense stationary stochastic processes.

Keywords:

• Fourier transform of a distribution
• jointly WSS