If you have watched all the 5 videos, congrats ! without doubt I can say that this is one of the best video series on z Transform in KZbin.
@beincheekym84 жыл бұрын
this is an amazing visualization, thank you so much, not only for this video but the whole series on Z-transform. It was eye-opening. Developed my own little version of Z-surface visualization in Python to nail it down in my head. I absolutely love this visualization of how S-space is just z-space when sampling frequency goes to infinity, quite bamboozled by it, making some nice connections in my brain.
@ddorran4 жыл бұрын
Thanks for the kind comment! Good luck with your studies!
@PunmasterSTP Жыл бұрын
I never thought of that either, and seeing it illustrated visually blew my mind.
@PunmasterSTP Жыл бұрын
The graphics were so succinct and insightful, and this was an amazing video!
@bassrabbit9 Жыл бұрын
Best explanation on this I have ever seen. Thank you for the colors!!
@ddorran Жыл бұрын
No problem! Glad it helped!
@felixw9185 Жыл бұрын
thank you so much, that video really helped to grow understanding:)
@andykandolf1948 Жыл бұрын
These are great videos 👍🙏🏻
@reaperromero76653 жыл бұрын
You blew my mind. :)
@oadka9 ай бұрын
Very nice comparison
@williamfehlhaber57085 жыл бұрын
woah... this is random. great explanation as usual!
@maria-js6sl4 жыл бұрын
Great vedeo
@hajerjm4 жыл бұрын
Amazing thanks
@AbhinavRao-te9co5 ай бұрын
Why is the region of stability within the unit circle for the Z Tranform? Isnt that where the signal grows exponentially i.e. instability?
@ddorran5 ай бұрын
You're correct (kind of!). The signal z^-n does grow exponentially for values of z that lie inside the unit circle. However, the z-transform multiplies the signal z^-n by the signal we are interested in analysing for stability e.g. x[n] (and then sums the resulting multiplied terms). If x[n] is growing exponentially and z^-n is also growing (which is the case for all values of z within the unit circle) then the sum of the products of x[n] and z[n] will never converge within the unit circle. On the other hand when x[n] is decaying and z^-n is growing then there will a set of values of z that lie within the unit circle for which the product of x[n] and he signal z^-n will converge. I suspect it's quite difficult to interpret these previous sentences - if so you could take a look at page 83 of www.researchgate.net/publication/370660126_The_z-transform_A_practical_overview or take the following video kzbin.info/www/bejne/mnatoWdsiKuajJY. Hopefully, one of these could provide some insight.
@AbhinavRao-te9co5 ай бұрын
@@ddorran I read the paper that you have linked, however I didnt understand one thing, you say that the region of convergence lies outside the circle with radius equal to that of the pole of the system. In your example you used -0.5. My question is why is it that you called -0.5 the pole? Wasn't that the impulse response? Also all of this implies that the region of stability/convergence is > Pole value circle, not that region of stability is
@ddorran5 ай бұрын
@@AbhinavRao-te9co "My question is why is it that you called -0.5 the pole?" The answer is because H(z) goes toward infinity when z= -0.5 (poles exist at values of z for which H(z) goes toward infinity). "Also all of this implies that the region of stability/convergence is > Pole value circle, not that region of stability is
@AbhinavRao-te9co5 ай бұрын
@@ddorran "Having said that, regions outside the unit circle are associated with instability because any pole outside the unit circle will cause the system to be unstable (since the unit circle will not lie in the region of convergence)." Is there any proof for this or should i just learn this as a given?
@ddorran5 ай бұрын
@@AbhinavRao-te9co I don't have a formal proof to hand but there must be one out there! There are a couple of aspects to look at: A formal proof that the region of convergence lies outside the pole furthest from the origin (or proof that the region of convergence cannot contain poles, is another way of saying this); A formal proof that an unstable system contains poles that lie outside the unit circle. If both of these can be proven then it follows that the unit circle will not lie in the region of convergence, for unstable causal systems.
@窦泽华4 жыл бұрын
Hi Bro. nice video! Would you like to tell me how you did the visulisation? thx in advance
@ddorran4 жыл бұрын
It's done in Matlab by creating guí objects and writing code to manipulate those objects.
@窦泽华4 жыл бұрын
@@ddorran thx bro😉😉😉
@kebabsharif96272 жыл бұрын
Please explain clearlly , what happend if the sampling time descrease?
@ddorran2 жыл бұрын
Good question. One way to picture this is to play the video backwards from the end up to time 1 min 55 sec! After this point (in reverse time) you'd have to use your imagination and picture that the yellow 'circle' points would continue to rotate past the -1+0j and become negative imaginary terms (aliased negative frequencies). Similarly, the red 'circle' points would rotate past the -1+0j and become positive imaginary terms (aliased positive frequencies). Eventually the green radial lines would also become associated with aliased negative frequencies - and if the sampling frequency continued to reduce eventually all the points that are associated with aliased negative frequencies would become aliased positive frequencies (and so on ).
@n4mmenam Жыл бұрын
🐐
@AbdulMoiz-kj6ut2 жыл бұрын
which book do u prefer ??
@ddorran Жыл бұрын
DSP Guide by Smith and Understanding DSP by Lyons. My notes aren't too bad either (see pzdsp.com/docs/)