g13cdf

Purpose

Synopsis

[xg,yg,ng,ifail] = g13cdf(nxy,is,l,xg,yg<,pxy,mw,mtxy,pw,ifail>)

Description

 
 The supplied time series may be mean and trend corrected and 
 tapered as in the description of G13CBF before calculation of the
 unsmoothed sample cross-spectrum
 
                     { n                  } { n                   }
  *              1   { --                 } { --                  }
 f  ((omega))= ------{ >  y exp(i(omega)t)}*{ >  x exp(-i(omega)t)}
  xy           2(pi)n{ --  t              } { --  t               }
                     { t=1                } { t=1                 }
 
                                2(pi)j                   
 for frequency values (omega) = ------, 0<=(omega) <=(pi).
                             j    K               j      
 
 A correction is made for bias due to any tapering.
 
 As in the description of G13CBF for univariate frequency window 
 smoothing, the smoothed spectrum is returned at a subset of these
 frequencies,
 
                         2(pi)l
                  (nu) = ------ , l=0,1,...,[L/2]
                      l    L   
 
 where [ ] denotes the integer part.
 
 Its real part or co-spectrum cf((nu) ), and imaginary part or 
                                     l                        
 quadrature spectrum qf((nu) ) are defined by
                            l              
 
 
      f  ((nu) )=cf((nu) )+iqf((nu) ) 
       xy     l         l          l  
          
                  --              ~  *       
                = >               w f  ((nu) +(omega) )
                  --               k xy     l        k
                              (pi)           
                  |(omega) |< ----           
                          k    M             
 
                   ~                                           
 where the weights w  are similar to the weights w  defined for 
                    k                             k            
 G13CBF, but allow for an implicit alignment shift S between the 
 series:
 
                      ~    
                      w =w exp(-2(pi)iSk/L).
                       k  k
 
 It is recommended that S is chosen as the lag k at which the 
 cross covariances c  (k) peak, so as to minimize bias.
                    xy                            
 
 If no smoothing is required, the integer M which determines the 
                         2(pi)                    
 frequency window width  -----, should be set to n.
                           M                      
 
 The bandwidth of the estimates will normally have been calculated
 in a previous call of G13CBF for estimating the univariate 
 spectra of y  and x .
             t      t
 

Parameters

g13cdf

Required Input Arguments:

nxy                                   integer
is                                    integer
l                                     integer
xg (:)                                real
yg (:)                                real

Optional Input Arguments:                       <Default>

pxy                                   real     0.0
mw                                    integer  nxy
mtxy                                  integer  0
pw                                    real     0
ifail                                 integer  -1

Output Arguments:

xg (:)                                real
yg (:)                                real
ng                                    integer
ifail                                 integer