hilbert
=======

Discrete-time analytic signal computation of a real signal using
Hilbert transform



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


::

    x=hilbert(xr)




Arguments
~~~~~~~~~

:xr real vector : the real signal samples
: :x Complex vector: the discrete-time analytic signal.
:



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

Returns theanalytic signal, from a real data sequence.

The analytic signal `x= xr + i*xi` has a real part, `xr`, which is the
original data, and an imaginary part, `xi`, which contains the Hilbert
transform. The imaginary part is a version of the original real
sequence with a 90° phase shift.



References
~~~~~~~~~~

``http://ieeexplore.ieee.org/iel5/78/16975/00782222.pdf?arnumber=78222
2`_`

Marple, S.L., "Computing the discrete-time analytic signal via FFT,"
IEEE Transactions on Signal Processing, Vol. 47, No.9 (September
1999), pp.2600-2603



See Also
~~~~~~~~


+ `window`_ compute symmetric window of various type
+ `hil`_ FIR approximation to a Hilbert transform filter




Examples
~~~~~~~~


::

    //compare the discrete-time analytic signal imaginary part of the impulse real signal 
    // with the FIR approximation of the Hilbert transform filter
    m=25;
    n=2*m+1;
    y=hilbert(`eye`_(n,1));
    h=`hilb`_(n)';
    h=[h((m+1):$);h(1:m)];
    `plot`_([`imag`_(y) h])


.. _http://ieeexplore.ieee.org/iel5/78/16975/00782222.pdf?arnumber=782222: http://ieeexplore.ieee.org/iel5/78/16975/00782222.pdf?arnumber=782222
.. _hil: hilb.html
.. _window: window.html