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