Optimal filtering in fractional Fourier domains

Image registration based on Fractional Fourier Transform

“…As fractional Fourier transform (FRFT) [3,4] is a generalization of the conventional Fourier transform and consists of spatial and frequency information, it is natural to extend its use in IR applications. Besides, the use of the FRFT is motivated by the observation in [5] that the optimum FRFT domain for noise elimination may be different from the conventional spatial or frequency domain.…”

A time-variant filtering approach for non-stationary random signals based on the fractional convolution

“…However, these methodologies may not be extendable to any problem, either by its nature or because they do not provide satisfactory results. From this need, efforts have focused on the description of a theory allowing the signal processing in fractional domains [17][18][19][20]. All these initiatives aim to propose an alternative solution with the important feature of maintaining a harmonic description of the problem.…”

Image representation and compression with the fractional Fourier transform

“…The fractional version of the optimal Wiener ®ltering problem has been studied in detail in Ref. [4]. Fractional Fourier-domain ®ltering has been further generalized to multi-stage and multi-channel ®ltering ( Fig.…”

“…1(a)±(c)) [3,4]. Fractional Fourier-domain ®ltering consists of (i) taking the fractional Fourier transform of the input signal, (ii) multiplication with a ®lter function, and (iii) taking the inverse fractional Fourier transform of the result.…”

“…The problem of ®nding the optimal ®lter coe cients, given the transform orders has been solved in Refs. [2,4,5] using a minimum mean square error approach. On the other hand, the problem of optimizing multiple orders has not yet been addressed, and in most cases the orders have been chosen uniformly.…”