Introduction - If you have any usage issues, please Google them yourself
time-invariant degradation models and stationary
signals and noise, the classical Fourier domain Wiener
filter, which can be implemented in O(N logN) 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(N2) 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 logN) 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.