SUKFRAC - apply FRACtional powers of i|k| to data, with phase shift sukfrac outfile [optional parameters] Optional parameters: power=0 exponent of (i*sqrt(k1^2 + k2^2))^power =0 ===> phase shift only >0 ===> differentiation <0 ===> integration sign=1 sign on transform exponent d1=1.0 x1 sampling interval d2=1.0 x2 sampling interval phasefac=0 phase shift by phase=phasefac*PI Notes: The relation: w = 2 pi F is well known for frequency, but there doesn't seem to be a commonly used letter corresponding to F for the spatial conjugate transform variables. We use K1 and K2 for this. More specifically we assume a phase: -i(k1 x1 + k2 x2) = -2 pi i(K1 x1 + K2 x2). and K1, K2 define our respective wavenumbers. Algorithm: g(x1,x2)=Re[2DINVFFT{ ( (sign) i |k|)^power 2DFFT(f)}e^i(phase)] Caveat: Large amplitude errors will result of the data set has too few points. Examples: Edge sharpening: Laplacean : sukfrac < image_data power=2 phasefac=-1 | ... Image enhancement: Derivative filter: sukfrac < image_data power=1 phasefac=-.5 | ... Image enhancement: Half derivative (this one is the best for photographs): sukfrac < image_data power=.5 phasefac=-.25 | ... Credits: CWP: John Stockwell, June 1997, based on sufrac. Trace header fields accessed: ns, d1, d2