c06fpf

Purpose

Synopsis

[x,trig,ifail] = c06fpf(x<,trig,init,ifail>)

Description

 
                                          p                    
 Given m sequences of n real data values x , for j=0,1,...,n-1; 
                                          j                    
 p=1,2,...,m, this routine simultaneously calculates the Fourier 
 transforms of all the sequences defined by:
 
            n-1                  
    ^p   1  --  p    (   2(pi)jk)
    z = --- >  x *exp(-i -------), k=0,1,...,n-1; p=1,2,...,m.
     k    _ --  j    (      n   )
        \/n j=0                  
 
                          1                     
 (Note the scale factor  --- in this definition.)
                           _                    
                         \/n                    
 
                        ^p                                     
 The transformed values z  are complex, but for each value of p 
                         k                                     
     ^p                                 ^p                 
 the z  form a Hermitian sequence (i.e.,z    is the complex 
      k                                  n-k               
              ^p                                               
 conjugate of z ), so they are completely determined by mn real 
               k                                               
 numbers (see also the Chapter Introduction).
 
 The discrete Fourier transform is sometimes defined using a 
 positive sign in the exponential term:
 
                          n-1                  
                  ^p   1  --  p    (   2(pi)jk)
                  z = --- >  x *exp(+i -------).
                   k    _ --  j    (      n   )
                      \/n j=0                  
 
 To compute this form, this routine should be followed by a call 
                                                 ^p
 to C06GQF to form the complex conjugates of the z .
                                                  k
 

Parameters

c06fpf

Required Input Arguments:

x (:,:)                               real

Optional Input Arguments:                       <Default>

trig (:)                              real     zeros(2*size(x,2),1)
init (1)                              string   c06fpf04(trig)
ifail                                 integer  -1

Output Arguments:

x (:,:)                               real
trig (:)                              real
ifail                                 integer