convol
======

convolution



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [y]=convol(h,x)
    [y,e1]=convol(h,x,e0)




Arguments
~~~~~~~~~

:h a vector, first input sequence ("short" one)
: :x a vector, second input sequence ( "long" one)
: :e0 a vector,old tail to overlap add (not used in first call)
: :y a vector, the convolution.
: :e1 new tail to overlap add (not used in last call)
:



Description
~~~~~~~~~~~

Calculates the convolution `y= h*x` of two discrete sequences by using
the fft. The convolution is defined as follow:



Overlap add method can be used.

USE OF OVERLAP ADD METHOD: For `x=[x1,x2,...,xNm1,xN]` First call is
`[y1,e1]=convol(h,x1);` Subsequent calls :
`[yk,ek]=convol(h,xk,ekm1)`; Final call : `[yN]=convol(h,xN,eNm1);`
Finally `y=[y1,y2,...,yNm1,yN]`.

The algorithm based on the convolution definition is implemented for
polynomial product: `y=convol(h,x)` is equivalent to
`y=coeff(poly(h,'z','c')*poly(x,'z','c')` but much more efficient if
`x` is a "long" array.



Examples
~~~~~~~~


::

    x=1:3;
    h1=[1,0,0,0,0];h2=[0,1,0,0,0];h3=[0,0,1,0,0];
    x1=convol(h1,x),x2=convol(h2,x),x3=convol(h3,x),
    convol(h1+h2+h3,x)
    p1=`poly`_(x,'x','coeff')
    p2=`poly`_(h1+h2+h3,'x','coeff')
    p1*p2




See Also
~~~~~~~~


+ `corr`_ correlation, covariance
+ `fft`_ fast Fourier transform.
+ `pspect`_ two sided cross-spectral estimate between 2 discrete time
  signals using the Welch's average periodogram method.


.. _fft: fft.html
.. _corr: corr.html
.. _pspect: pspect.html