SUKFRAC - apply FRACtional powers of i|k| to data, with phase shift 

     sukfrac <infile >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