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# cspect

two sided cross-spectral estimate between 2 discrete time signals using the correlation method

### Calling Sequence

[sm [,cwp]]=cspect(nlags,npoints,wtype,x [,y] [,wpar]) [sm [,cwp]]=cspect(nlags,npoints,wtype,nx [,ny] [,wpar])

### Arguments

- x
vector, the data of the first signal.

- y
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 numer of element than`x.`

- nx
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).- ny
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`

.- nlags
number of correlation lags (positive integer)

- npoints
number of transform points (positive integer)

- wtype
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

- wpar
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`

- sm
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.- cwp
the unspecified Chebyshev window parameter in case of Chebyshev windowing, or an empty matrix.

### Description

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, the`x`

and
`y`

data may be read segment by segment using the
`getx`

and `gety`

user defined
functions. These functions have the following calling sequence:

`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.

### Warning

For Scilab version up to 5.0.2 the returned value was the modulus of the current one.

### Reference

Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing, Upper Saddle River, NJ: Prentice-Hall, 1999

### Examples

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))

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