c06ekf

Purpose

Synopsis

[x,y,ifail] = c06ekf(job,x,y<,ifail>)

Description

 
 This routine computes:
 
 if JOB =1, the discrete convolution of x and y, defined by:
 
                         n-1        n-1      
                         --         --       
                     z = >  x y   = >  x   y ;
                      k  --  j k-j  --  k-j j
                         j=0        j=0      
 
 if JOB =2, the discrete correlation of x and y defined by:
 
                              n-1      
                              --       
                          w = >  x y   .
                           k  --  j k+j
                              j=0      
 
 Here x and y are real vectors, assumed to be periodic, with 
 period n, i.e., x =x    =x     =...; z and w are then also 
                  j  j+-n  j+-2n                           
 periodic with period n.
 
    ^  ^  ^     ^                                             
 If x, y, z and w are the discrete Fourier transforms of these 
 sequences,
 
               n-1                    
       ^    1  --       (   2(pi)jk)  
 i.e., x = --- >  x *exp(-i -------), etc,
        k    _ --  j    (      n   )  
           \/n j=0                    
 
       ^    _ ^ ^
 then  z =\/n.x y 
        k      k k
 
              _  
       ^    _ ^ ^
 and   w =\/n.x y 
        k      k k
 
 (the bar denoting complex conjugate).
 
 This routine calls the same auxiliary routines as C06EAF and 
 C06EBF to compute discrete Fourier transforms, and there are some
 restrictions on the value of n.
 

Parameters

c06ekf

Required Input Arguments:

job                                   integer
x (:)                                 real
y (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

x (:)                                 real
y (:)                                 real
ifail                                 integer