Abstract
The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum mean square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
