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..
On Sun, Aug 17, 2014 at 10:45 PM, Ali <user0...@gmail.com> wrote: > Thanx Marcus and Tom fr ur explanations. I will read further and ask any > questions if i have. > > > > > Tom Rondeau <t...@trondeau.com> wrote: > > > On Sun, Aug 17, 2014 at 11:04 AM, jason sam <user0...@gmail.com> 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 Discuss-gnuradio@gnu.org https://lists.gnu.org/mailman/listinfo/discuss-gnuradio
