two sided cross-spectral estimate between 2 discrete time signals using the correlation method
[sm [,cwp]]=cspect(nlags,npoints,wtype,x [,y] [,wpar]) [sm [,cwp]]=cspect(nlags,npoints,wtype,nx [,ny] [,wpar])
vector, the data of the first signal.
vector, the data of the second signal. If y
is omitted it is supposed to be equal to x
(auto-correlation). If it is present, it must have the same number of
element than x.
a scalar : the number of points in the x
signal. In this case the segments of the x signal are loaded by a
user defined function named getx
(see
below).
a scalar : the number of points in the
y
signal. In this case the segments of
the y
signal are loaded by a user defined
function named gety
(see below). If
present ny
must be equal to
nx
.
number of correlation lags (positive integer)
number of transform points (positive integer)
The window type
're'
: rectangular
'tr'
: triangular
'hm'
: Hamming
'hn'
: Hann
'kr'
: Kaiser,in this case the wpar
argument must be given
'ch'
: Chebyshev, in this case the wpar
argument must be given
optional parameters for Kaiser and Chebyshev
windows:
'kr': wpar must be a strictly positive
number
'ch': wpar
must be a 2 element vector
[main_lobe_width,side_lobe_height]with
0<main_lobe_width<.5
, and
side_lobe_height>0
The power spectral estimate in the interval
[0,1]
of the normalized frequencies. It
is a row array of size npoints
. The array
is real in case of auto-correlation and complex in case of
cross-correlation.
the unspecified Chebyshev window parameter in case of Chebyshev windowing, or an empty matrix.
Computes the cross-spectrum estimate of two signals
x
and y
if both are given and the
auto-spectral estimate of x
otherwise. Spectral
estimate obtained using the correlation method.
The cross spectrum of two signal x and y is defined to be
The correlation method calculates the spectral estimate as the Fourier transform of a modified estimate of the auto/cross correlation function. This auto/cross correlation modified estimate consist of repeatedly calculating estimates of the autocorrelation function from overlapping sub-segments if the data, and then averaging these estimates to obtain the result.
The number of points of the window is
2*nlags-1.
For batch processing, thex
and
y
data may be read segment by segment using the
getx
and gety
user defined
functions. These functions have the following syntax:
xk=getx(ns,offset)
and
yk=gety(ns,offset)
where ns
is the
segment size and offset
is the index of the first
element of the segment in the full signal.
For Scilab version up to 5.0.2 the returned value was the modulus of the current one.
Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing, Upper Saddle River, NJ: Prentice-Hall, 1999
rand('normal');rand('seed',0); x=rand(1:1024-33+1); //make low-pass filter with eqfir nf=33;bedge=[0 .1;.125 .5];des=[1 0];wate=[1 1]; h=eqfir(nf,bedge,des,wate); //filter white data to obtain colored data h1=[h 0*ones(1:max(size(x))-1)]; x1=[x 0*ones(1:max(size(h))-1)]; hf=fft(h1,-1); xf=fft(x1,-1);yf=hf.*xf;y=real(fft(yf,1)); sm=cspect(100,200,'tr',y); smsize=max(size(sm));fr=(1:smsize)/smsize; plot(fr,log(sm)) | ![]() | ![]() |