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])