Abstract
An analytical expression for the probability density function (PDF) of a random process power spectrum value at a given frequency is derived. The significance of the derived PDF relates to cases where incomplete process realizations are available for power spectrum estimation applications. Specifically, standard power spectrum estimation techniques subject to missing data such as zero-padding and least squares regression normally provide with a deterministic estimate for the power spectrum value at a given frequency. In this regard, no information is provided concerning the uncertainty in the estimates. In this paper, relying on the assumptions of stationarity and ergodicity, and on minimum assumptions about the missing data, an explicit closed-form analytical expression for the PDF of the power spectrum value at each and every frequency is derived. In this manner, the uncertainty propagation from the measured incomplete process realization in the time/space domain to its power spectrum estimate in the frequency domain is efficiently quantified. Further, the derived results can be potentially used for assessing the performance of alternative power spectrum estimation techniques subject to missing data which provide with a deterministic estimate for the power spectrum value at a specific frequency.
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.