Browsing by Subject "Wiener filter"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Optimal filtering in fractional Fourier domains
    (Institute of Electrical and Electronics Engineers, 1997-05) Kutay, M. A.; Özaktaş, Haldun M.; Arıkan, Orhan
    For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N/sup 2/) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N log N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained.
  • Thumbnail Image
    ItemUnknown
    Optimal fractional fourier filtering for graph signals
    (IEEE, 2021-05-19) Öztürk, Cüneyd; Özaktaş, Haldun M.; Gezici, Sinan; Koç, Aykut
    Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.