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Re: [Discuss-gnuradio] Hilbert transform

From: jason sam
Subject: Re: [Discuss-gnuradio] Hilbert transform
Date: Mon, 18 Aug 2014 20:22:51 +0500

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 <address@hidden> wrote:
> Thanx Marcus and Tom fr ur explanations. I will read further and ask any 
> questions if i have.
> Tom Rondeau <address@hidden> wrote:
> On Sun, Aug 17, 2014 at 11:04 AM, jason sam <address@hidden> 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

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