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])




Arguments
~~~~~~~~~

: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 `D` is 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'`: 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 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:`max`_(`size`_(x))-1)];
    x1=[x 0*`ones`_(1:`max`_(`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=`max`_(`size`_(hf2));fr=(1:hsize)/hsize;`plot`_(fr,`log`_(hf2));
    
    //pspect example
    sm=pspect(100,200,'tr',y);smsize=`max`_(`size`_(sm));fr=(1:smsize)/smsize;
    `plot`_(fr,`log`_(sm));
    `rand`_('unif');




See Also
~~~~~~~~


+ `cspect`_ two sided cross-spectral estimate between 2 discrete time
  signals using the correlation method
+ `pspect`_ two sided cross-spectral estimate between 2 discrete time
  signals using the Welch's average periodogram method.
+ `mese`_ maximum entropy spectral estimation
+ `window`_ compute symmetric window of various type


.. _mese: mese.html
.. _pspect: pspect.html
.. _cspect: cspect.html
.. _window: window.html