What's the function of group delay and it relation to linear phase?

Dear all:
In filter design , we need to take care "group delay".
In filter book , it just only say linear phase for good group delay.
But I still don't know linear phase have any profit and group delay
have any mean ?
Somebody can tell me ?

thanks.

about group delay

group delay is the time it takes the information to show up at the other end of your t-line, typically signals travel at the speed of light, but information doesn't necessarily follow this pattern. linear phase is good because sometimes different components of your signal have different freqs and nonlinear phase will cause spreading or delay of particular parts.

Re: about group delay

super,
If a system has linear phase, then its phase shift is proportional to frequency. The result is that waveforms that consist of multiple frequency components suffer no waveform distortion. They only experience a delay. You can demonstrate this by generating a waveform (in Excel, for example) that consists of a fundamental and a third harmonic. Shift the phase of the fudamental by X degrees. Shift the phase of the third harmonic by 3X degrees. The sum will be a waveform that is delayed, but has exactly the same shape is the original.
Regards,
Kral

about group delay

Good question, good reply
In one word in my opion, linear phase does't bring signal distortion.

Re: about group delay

your can refer to pg.89 of Bruce Carlson (Communication Systems -4th Edition) for a good discussion on the topic - the book can be downloaded from the downloads sections.

In time domain, we know that "The output is undistorted if it differs from the input only by a multiplying CONSTANT and a finite time delay".

Clearly, whenever a signal passes through a system, it must incur some delay. This constant time delay, in frequency domain (you must've studied with Fourier Transform) becomes a LINEAR PHASE SHIFT (linearly related to frequency)....

Let us take an example where a signal suffers from a CONSTANT PHASE SHIFT, i.e. let us assume that all its frequency components incur a phase shift of 70°. Now in time domain, if the frequency component with a frequency of 'x' kHz has a delay of 3 microseconds (corresponds to 70 degrees), then the frequency component with a frequency of '3x' kHz will have a delay of 1 microseconds (corresponding to 70 degrees, i.e. (70/360)*Timeperiod_of_3x_kHz)....Thus due to CONSTANT PHASE SHIFT, different frequency components of the same signal suffer from DIFFERENT TIME DELAYS....which definitely causes distortion, b/c each frequency component has a different tim period...

On the other hand, if the signal suffers from a LINEAR PHASE SHIFT, phase shift proportional to frequency, then the 'x' kHz signal will suffer from the same time delay as the '3x' kHz signal component.

This got a bit complicated....but still I hope it helps...

Re: about group delay

Thanks everyone give me so good explain.
I have do the simulation that Kral and zeeshanzia84 advise .
In time domain , I can see the distortion when phase have difference each of them in fundamental and 3rd harmonic.
In spectrum domain, there is no difference when phase have large shift or small shift or fundamental shift x degree 3rd shift 3x degree, is that result is right ?

And I will continued to study pg.89 of Bruce Carlson (Communication Systems )
this topic that zeeshanzia84 suggestion.


Thanks.

Re: about group delay

Although I don't understand you completely, I think your results are correct.

If you are just watching the AMPLITUDE SPECTRUM, it will not have any difference. However, the PHASE SPECTRUM will show you the phase shift (in radians or degrees) that each frequency component suffers from.

about group delay

Dear zeeshanzia84 :
I'm so stupid, I don't know that " PHASE SPECTRUM " what you said.
How to sim " PHASE SPECTRUM " ?

thanks.

Re: about group delay

which tool are you using for your simulation? Matlab??? or something related to Analog design like Virtuoso?

about group delay

I use cadence Virtuoso .