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.