pspect

Name

pspect — two sided cross-spectral estimate between 2 discrete time signals using the Welch's average periodogram method.

Calling Sequence

      [sm [,cwp]]=pspect(sec_step,sec_leng,wtype,x [,y] [,wpar])
      [sm [,cwp]]=pspect(sec_step,sec_leng,wtype,nx [,ny] [,wpar])

Parameters

x

vector, the time-domain samples of the first signal.

y

vector, the time-domain samples 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 samples 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 samples 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.

sec_step

offset of each data window. The overlap Dis given by sec_leng -sec_step. if sec_step==sec_leng/2 50% overlap is made. The overlap

sec_leng

Number of points of the window.

wtype

The window type

're': rectangular
'tr': triangular
'hm': Hamming
'hn' : Hanning
'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]with0<main_lobe_width<.5, and side_lobe_height>0

sm

Two sided power spectral estimate in the interval [0,1] of the normalized frequencies. It is a row array with sec_len elements . The array is real in case of auto-correlation and complex in case of cross-correlation.

The associated normalized frequencies array is linspace(0,1,sec_len).

cwp

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 modified periodogram method.

The cross spectrum of two signal x and y is defined to be

The modified periodogram method of spectral estimation repeatedly calculates the periodogram of windowed sub-sections of the data containes in x and y . These periodograms are then averaged together and normalized by an appropriate constant to obtain the final spectral estimate. It is the averaging process which reduces the variance in the estimate.

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.

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:maxi(size(x))-1)];
x1=[x 0*ones(1:maxi(size(h))-1)];
hf=fft(h1,-1); xf=fft(x1,-1);y=real(fft(hf.*xf,1));

//plot magnitude of filter
h2=[h 0*ones(1:968)];hf2=fft(h2,-1);hf2=real(hf2.*conj(hf2));
hsize=maxi(size(hf2));fr=(1:hsize)/hsize;plot(fr,log(hf2));

//pspect example
sm=pspect(100,200,'tr',y);smsize=maxi(size(sm));fr=(1:smsize)/smsize;
plot(fr,log(sm));
rand('unif');

Authors

C. Bunks INRIA