Abstract
A new representation, called an exponential Fourier density, of a probability density on a circle, S^{1} is introduced. It is shown that a density of bounded variation on S^{1} can be approximated as closely as desired by such a representation in the space of square-integrable functions on S^{1} . The exponential Fourier densities have the desirable feature of being closed under the operation of taking conditional distributions. Facilitated by the use of these densities, finite-dimensional, recursive, and optimal estimation and detection schemes are derived for some simple models including a PSK communication system. A deficiency of the exponential Fourier densities is that they are not closed under convolution. How to circumvent this deficiency is still an open question.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.