Help for FFT1PIX

 FFT1PIX  is  a  VICAR application program which works in conjunction
 with  FFT1  to  allow  the user to display and/or modify the Fourier
 transform  using  existing VICAR programs.  The procedure is similar
 to  that  used  in  FFT2,  FFTPIC,  and  TPIKMASK  but  without  the
 restriction  that  terms  of  the transform be either set to zero or
 left  unchanged.   In  the forward mode, the input to fft1pix is the
 complex Fourier transform from FFT1.  The output can be an amplitude
 picture  and/or a phase picture of the transform.  Those can then be
 modified to the users needs and re-inputed to fft1pix in the reverse
 mode.   The  Fourier transform is then modified in accordance to the
 changes made to the amplitude and/or phase pictures.
 Let

 z(k) = a(k) + ib(k) 
 
 be  the  k'th  term  of  the  Fourier  series  of a given line.  The
 amplitude   of   this   term   is   |z|   and  the  phase  angle  is
 atan(b(k)/a(k)).   Then  the  DN of the k'th sample in the amplitude
 picture equals is p*|z|, where p is a scaling factor.

 If  the log option is used, DN = p*LOG(|z|).  p is determined by the
 normalization  options  used.  Similarly the DN of the phase picture
 is given by:

 DN = q * (phase angle) + s

 where q and s are scaling factors.  If NOSIGN is requested,

 DN = q * |phase angle| + s.

 If  requested, then the amplitude and phase pictures are written out
 on  the primary and secondary output data sets.  In addition, a page
 plot of the amplitudes may be printed on the line printer, providing
 a  means  of accurately locating noise spikes in the transform.  The
 user  may  now  modify the amplitude or phase picture using existing
 VICAR programs.  For example, Noise spikes may be QSAR'ed out of the
 amplitude picture.

 The  modified  amplitude  and  phase  pictures are now re-input into
 fft1pix  in  the  reverse  mode.   The  complex*8 transform data set
 remains  as  the  primary  input, the modified amplitude picture the
 secondary input, and the modified phase picture the third input.  If
 the amplitude or phase picture was not modified, then it need not be
 re-input  to  fft1pix.   Each  term  of  the  original  transform is
 compared  to  the  corresponding  term of the modified amplitude and
 phase  pictures; if the amplitude differs, the term is recomputed to
 match  that of the amplitude picture with phase angle preserved.  If
 the  phase  angle  differs  from  the  phase  picture,  the  term is
 recomputed  to match the new phase angle, amplitude preserved.  Thus
 the  user  has complete control over each term of the transform.  If
 CONJ  is not specified in the reverse mode, the complex conjugate of
 a  term  is  automatically  modified  in the identical manner to its
 conjugate  term.   The output is a complex*8 data set containing the
 Fourier  transform  after  modifications  have  been made to it.  If
 requested,  a page plot is made of the transform after modification.

 The modified transform is now ready to be input into FFT1 in inverse
 mode to produce the resulting image.

 WRITTEN BY : 			JOHN ADDINGTON
 COGNIZANT PROGRAMMER : 	FLORANCE MOSS
 REVISION : 			04 JAN 1993
 CONVERTED TO VAX    BY:  	F. F. Moss,    20 JAN 1984
 CONVERTED TO VICAR2 BY:  	D. F. Stanfill,   JUN 1987
 PORTED BY:			J. F. McNeill, 04 JAN 1993

				J. F. McNeill, 22 JUL 1994
				Corrected printing of integer
				within PPLOT subroutine.
				(FR 85096)

 TIMING : Average CPU time used on VAX 8650 = 00:00:02.41.
	  Computed from TSTFFT1PIX.PDF for ported version 04 JAN 1993.