Region of Convergence for the z-Transform
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- เผยแพร่เมื่อ 21 ส.ค. 2024
- z-transforms of signals in general do not exist over the entire z-plane. The infinite series defining the z-transform only converges for a subset of values of z, termed the region of convergence. Multiple examples of deriving z-tranforms.
Why can't lectures try to be like you? Thanks, you are awesome.
I will try to clarify my use of terms:
1) A causal signal has x[n] = 0 for n
We say this signal is non causal by viewing it as if it were the impulse response of an LTI system. The impulse response of a causal system must be zero for n
You have such a great talent for teaching. Thank you veeery muuchhh for saving my final exam!
in case 3 the plot is wrong. For y[n]=-α^n u[-n -1] , with 0 < α < 1 the sequence should grow unbounded as n decreases.
Yes you are true. The sequence will grow unbounded. For the decaying sequence as shown in Figure, it should have been a>1
Thanks, this comment should be pushed front
I think it should -a^-n instead of -a^n
By far the best ROC explanation I've found. Thanks
The grt than1/4 applies to the first term alone in g[n] while less than 1/2 applies to the second term in g[n]. Hence for the z-transform of g[n] to converge, we can only include values of z for which BOTH terms in g[n] converge. This leads to the overall ROC being the INTERSECTION of grt than1/4 and less than 1/2, which results in the ring. I think it is easier to figure this out by looking at the individual terms. With a sum of signals the ROC will be the intersection of individ ROCs.
I could almost feel my hair blowing as your explanation at 13:15 flew right over my head lol.
Klae G's
haha 🤣🤣🤣
@@ShrenikJain i saw your videos. well, some people upload for sharing knowledge. and some like u open an online so-called last hours tuition school to make money lol
you should have clarified on how to choose region of convergence in examples rather than in general. I am not clear with the explanation.
At 11:46 how and why are they different? : |z|>1/4 but |z|
wait, u wrote my signals book ?
Beginner here, what's u[n] ? It's in the X[n] equation at the start but it's there anymore when we switch to the X(z) form. Thanks
Thank you so so much for posting these videos!
Not that i'm an expert either but it's not non causal, its anti causal.
A causal system can be past and present values, where a noncausal contains future values.
I think the anticausal system is a subcategory for only past values, referring to what mr. Van Ven commented at the top.
Feel free to correct me if im wrong.
Your videos are awesome, keep doing great work.
Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically? Are we supposed to manipulate our O/P by multiplying any signal from ROC such that our O/P converges & system is stable? And what if our signal is exponentially decaying so whats the purpose of finding ROC in this case (except for determing stability/casuality)?
you are a life saver
thank you for the for this vid you saved me from failing my semestre
What is the formula of u[n] in 3:26 such the a variable's value determes the value of x[n] such a way in each case,i don't understand.
And why in 4:36 when you aply the z transform formula on to x[n] you write Sum n-oo to +oo a^n*z^-n instead of Sum -oo to +oo a^n*u[n]*z^-n suposed the x[n] is a^n*u[n] not only a^n ?
I don't understand this neither.
Great explanation, thanks a lot for the effort.
Thank you sir, very nicely explained
I kind of got the idea of ROC but I have problem of knowing the casual and causal functions. I mean I can't really say if a series function is greater or smaller than alpha.
thank you very much sir for this explained
THANK YOU SIR. best VIDEO FOR UNDERSTANDING ROC
helped me a lot.. thanks
Hi Sir, in the last example, when you rewrite, is it
x[n] = u[n] +delta[n] - (-3/4)^n*u[-n-1] ?
isn't it x[n] = u[n] - delta[n] + (-3/4)^n*u[-n-1] ?
From your notation, two ways(before rewrite, after rewrite) of expression x[-1] will be
x[n] = (-3/4)^-1 , x[n] = - (-3/4)^-1
I'm a bit confused on this stuff. I really do love your videos. Thank you so much
Note that at 13:15 the expression is x[n] = u[n] +delta[n] - - (-3/4)^n*u[-n-1], that is there are two negative signs in between the delta[n] and (-3/4)^n terms and thus it is effectively a +. In your equation above you missed the second minus sign. You also have a - in front of delta[n], and that should be +. We can check as follows:
x[-1] = - - (-3/4)^(-1) = (-3/4)^(-1) which agrees before and after the rewrite step.
Also,
x[0] = u[0] +(-3/4)^0 u[0] = 2 (before the rewrite step) and
x[0] = u[0] + delta[0] = 2 (after the rewrite step).
I think the algebra is ok as written, but that is a good question - you are paying very close attention.
Barry Van Veen Ohh,, I see now. It wasn't tricky. I was just missing one negative sign. Thank you so much Sir.
I wish more students and people can find this channel and benefit from this great lectures. I found a month before the final which is tomorrow while have been suffering for couple months from ...well.
Appreciate your great effort.
Barry Van Veen thank you for explaining ......got confused also
great video. really helpful. thank you!!!
Hi! This should be obvious, but in Case 2, why is x[n]=0 for negative values of n?
Is u[n] a predefined function?
Thank you!
yes
very accurate and choice. i'm officialy a fan
thank you so much.
thank you
how do you know if a series is converging or not ?
Why do we assume the radius to be alpha?
at 14:19 i did not get the roc condition.
shouldnt it be z> -3/4
our only condition for infinite geometric series is that it should exist ...i.e denominator should not become zero or negative?
pritesh parikh
see it's |z| and not just z.
so you are right z >-3/4
so..... |z|
Thank you !!!
How do I know if its case 2 or 3 when I'm doing the inverse z transform table look up?
You must check the ROC.... if |z|>|α|, it is a right sided sequence α^n u[n]. if |z|
ty so much
why did delta[n] appear at 13.24? could anyone explain that properly? thankx
- A non causal signal has x[n] not equal 0 for some value n
Alpha can be complex so it would be better if you had written |alpha|
thanks a lot sir :)
helpfull thanx
Great explanation .!! can you tell me on 13:15 ... why are you using DETA ?
Hi, To convert sequence2 into a "anti causal sequence". So anti causal sequence is a sequence where there are values only for n
Not clear seen
It's ZED, no "Zee"
James
it changed over period
so now it's zee
you sck bro