c06eaf

Purpose

Synopsis

[x,ifail] = c06eaf(x<,ifail>)

Description

 
 Given a sequence of n real data values x , for j=0,1,...,n-1, 
                                         j                    
 this routine calculates their discrete Fourier transform defined 
 by:
 
                   n-1                  
           ^    1  --       (   2(pi)jk)
           z = --- >  x *exp(-i -------), k=0,1,...,n-1.
            k    _ --  j    (      n   )
               \/n j=0                  
 
                             1                          
 (Note the scale factor of  --- in this definition.) The 
                              _                         
                            \/n                         
                    ^                                        
 transformed values z  are complex, but they form a Hermitian 
                     k                                       
                 ^                                ^            
 sequence (i.e., z    is the complex conjugate of z ), so they are
                  n-k                              k           
 completely determined by n real numbers (see also the Chapter 
 Introduction).
 
 To compute the inverse discrete Fourier transform defined by:
 
                          n-1                  
                  ^    1  --       (   2(pi)jk)
                  w = --- >  x *exp(+i -------),
                   k    _ --  j    (      n   )
                      \/n j=0                  
 
 this routine should be followed by a call of C06GBF to form the 
                           ^ 
 complex conjugates of the z .
                            k
 
 There are some restrictions on the value of n.
 

Parameters

c06eaf

Required Input Arguments:

x (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

x (:)                                 real
ifail                                 integer