On Mon, Aug 18, 2014 at 11:22 AM, jason sam <[email protected]> wrote:
> Hi Tom, > As hilbert transform is a high-pass filter which only allows the > positive frequency components.And we know that only a complex signal > can have a single sided spectrum,not a real signal.So, i am still > confused that why the signal isn't showing any imaginary part??May b i > am not understanding fully.. Not sure. I think you definitely understand the concept. By removing the negative frequencies, you /must/ add an imaginary part to the complex signal. Basically, the Hilbert, as you understand, essentially just adds the appropriate imaginary part. I just tried your example, and things looked fine for me: http://imgur.com/z305wlS Tom > On Sun, Aug 17, 2014 at 10:45 PM, Ali <[email protected]> wrote: > > Thanx Marcus and Tom fr ur explanations. I will read further and ask any > questions if i have. > > > > > > > > > > Tom Rondeau <[email protected]> wrote: > > > > > > On Sun, Aug 17, 2014 at 11:04 AM, jason sam <[email protected]> wrote: > >> > >> Hi, > >> I have made a simple flowgraph as attached.I have on query that when i > >> observe the signal coming out of the 'Hilbert transform' block using a > >> time sink then its imaginary part is shown to be zero.According to the > >> theory the hilbert transform of a signal x(t) is: > >> x(t)+jx~(t) > >> where x~(t) is the quadrature phase component of x(t).Then why is the > >> signal from the hilbert block has zero imaginary part?? > >> Regards, > >> Ali > > > > > > > > The Hilbert transforms a real signal into an analytic signal. Think > about your case this way: you start with a real sine wave, so in the > frequency domain, you have a delta function at +f and -f. But if you have > that same sine way as a complex number, then you'll only have a delta at > +f. A sine wave travels along the unit circle, but in which direction? A > complex (analytic) signal gives you the value and the direction, like a > vector instead of a scalar. So we've reduce the ambiguity of the solution > by providing the direction: clockwise or counter clockwise. > > > > The Hilbert transforms the signal from real to complex by removing the > values in the negative frequency. In fact, most HIlbert transforms (like > the one here in GR) are just high-pass filters with the passband starting > at 0 Hz that provide this conversion process. > > > > I wrote a post showing the Hilbert transform effects without actually > explaining it. Still, it might be helpful to understand it: > > > > > http://www.trondeau.com/blog/2013/9/26/hilbert-transform-and-windowing.html > > > > Tom > > > > > > >
_______________________________________________ Discuss-gnuradio mailing list [email protected] https://lists.gnu.org/mailman/listinfo/discuss-gnuradio
