Thank you Dr. Ed Doering for the great and easy way of understanding of group delay. I want to highlight the importance of giving an example of group delay in physical matters, like you did on the very last slide. Wish you have a great life !
Great question! After some digging on this issue: Group delay is more precisely defined in terms of the *argument* (abbreviated "arg") of the complex exponential. Consequently when you write H(e^jω) in the form A(e^jω)e^j(arg), the "A" function can go negative as you correctly stated (and add a step discontinuity of plus/minus pi to the phase), but the "arg" function is independent of this discontinuity. At 6:15 I should have identified -2ω as "arg(H(e^jω)" instead of as the phase function.
Sure, try it this way: Suppose you apply an impulse function to a smoothing filter that has zero group delay. Further suppose the impulse response of the filter is 5 samples wide and symmetrical. If the impulse (a single non-zero sample) is located at time n=0 you will see that the output begins at n=-2 and ends at n=+2, that is, it is centered about the impulse. The filter smooths the impulse input (blurs/spreads it out) but does so without adding an additional delay. This sort of smoothing filter would be called "non-causal." The same smoothing action could be accomplished by a "causal" filter (output does not begin before the impulse is applied), too, but you will see the that the output must be delayed (that's the group delay calculation) so that the first non-zero output happens at n=0 instead of n=-2. Hope that helps!
Should the sum of exponentials not only be real-valued but also positive, in order to say that the phase of the signal is -2ω? Otherwise, any negative value in that sum should add phase to the system...
What is a transient, mentioned at the very end of this video? The "center" of the filter? Something like the "center" of the filter? (But then, why isn't it 2.5 for a filter of length 5?)
+Patrick Mullan Transient is the transient time of output signal before stead state i.e. 1. Given example is for discrete signal which exists only at integers time, Therefore 2.5 does not exist at all. For continuous case it would be 2.5. In given example there are 5 point 0,1,2,3,4, it is quite obvious that 2 is in center.
Thank you Dr. Ed Doering for the great and easy way of understanding of group delay. I want to highlight the importance of giving an example of group delay in physical matters, like you did on the very last slide. Wish you have a great life !
Wow. I love how the algebra is instantly updated as you're explaining it. Great work!
Great question! After some digging on this issue: Group delay is more precisely defined in terms of the *argument* (abbreviated "arg") of the complex exponential. Consequently when you write H(e^jω) in the form A(e^jω)e^j(arg), the "A" function can go negative as you correctly stated (and add a step discontinuity of plus/minus pi to the phase), but the "arg" function is independent of this discontinuity. At 6:15 I should have identified -2ω as "arg(H(e^jω)" instead of as the phase function.
A very concise and straight forward introduction to group delay. Thanks!
Thanks for your kind remarks, glad to hear that you found the tutorial helpful!
-- Ed D
Good video and clarification on the comments. Thanks
Very well explained and also good pace for the video
Best explanation out there. Thank you.
Way more better than my lecturer.
Great video, thanks!
Thanks. The x[n] = u[n] example was very helpful.
You are a great teacher, thx a lot!
Nice tutorial! Thank you.
I just don't understand your last explanation of the physical significance of T(w)=2samples . Would you consider elaborating the same ??
Sure, try it this way: Suppose you apply an impulse function to a smoothing filter that has zero group delay. Further suppose the impulse response of the filter is 5 samples wide and symmetrical. If the impulse (a single non-zero sample) is located at time n=0 you will see that the output begins at n=-2 and ends at n=+2, that is, it is centered about the impulse. The filter smooths the impulse input (blurs/spreads it out) but does so without adding an additional delay. This sort of smoothing filter would be called "non-causal." The same smoothing action could be accomplished by a "causal" filter (output does not begin before the impulse is applied), too, but you will see the that the output must be delayed (that's the group delay calculation) so that the first non-zero output happens at n=0 instead of n=-2. Hope that helps!
Thank you very much sir.
That was clear as hell! Thanks!
Very well done! Thank you so much!
Very good tutorial thank you.
Should the sum of exponentials not only be real-valued but also positive, in order to say that the phase of the signal is -2ω? Otherwise, any negative value in that sum should add phase to the system...
What is center of transient in 2nd example?
Very good
Love you man!
Great Video!!!
What is a transient, mentioned at the very end of this video?
The "center" of the filter? Something like the "center" of the filter? (But then, why isn't it 2.5 for a filter of length 5?)
+Patrick Mullan Transient is the transient time of output signal before stead state i.e. 1. Given example is for discrete signal which exists only at integers time, Therefore 2.5 does not exist at all. For continuous case it would be 2.5. In given example there are 5 point 0,1,2,3,4, it is quite obvious that 2 is in center.
Thank you!
thanks
Why did I go the Bradley. I should've went to Rose-Hulman
6:09 real values? how come?
Because you can express what is inside of the parenthesis as 1+2cos(w)+2cos(2w)