Subroutine for continuous cross spectrum analysis of two

one-dimensional series x(i) and y(i) (i=1,...,n).

Input parameters and arrays: n,m, x(n), y(n),

n: number of data

m: biggest lag time length. Generally, m is between n/3 and n/10.

x(n),y(n): raw series

Output variables:

ol(0:m): frequency array

tl(0:m): periodic array

px(0:m): power spectrum of x(n)

py(0:m): power spectrum of y(n)

pxy(0:m): co-spectrum between x and y

qxy(0:m): quad-spectrum between x and y

rxy(0:m): coherence spectrum between x and y (it is between 0 and 1)

cxy(0:m): phase difference spectrum between x and y

If cxy(i)>0, then x trails y for the wave i, i.e. y leads x.

lxy(0:m): lag length spectrum between x and y

rxy951(0:m): 95 F-test confidence upper limit for coherence spectrum rxy

rxy952(0:m): 95 Goodman-test confidence upper limit for coherence spectrum rxy - By Dr. Li Jianping, September 6, 2001.