Hi can I ask a question about having a term like this: A/(1-dk*z^1)^L If L = 4 would that make the inverse z transform: A[(n+1)*(n+2)*(n+3)/3!]*dk^n*u[n] also, would u[n] be a delta function?
Hello! Are you familiar with the term "linear Fractional Transformation?" Could you please tell me about any book or published document using the term "Linear Fractional Transformation?" I have a video entitled "Inverse of linear ratio (Ax+B) /(Cx+D) is: (-Dx+B) / (Cx-A). Believe it or not but I thought that I was the first person to have discovered this fact but someone sent me the following link where I found my discovery on page 4 of the class assignment. I went to the copyright office and could not find anything with "linear Fractional Transformation" in the title. Thank you!
+Barry Van Veen At 9:45, why does the pole at z = -2 give rise to a non-causal z inverse transform, whereas the pole at -z = 1 gives rise to a causal z inverse transform? I thought the system was causal only for values INSIDE the ROC. Also you said in the video that z = 1/2 gives rise to a causal z inverse transform?? I thought the systems was causal for 1
@@jamesduffin3839 I think I see the confusion. The earlier part of the video did suggest what you've said, however, I think that you need to compare the magnitude of z within the ROC: 1 < |z| < 2, with the magnitude of each pole. e.g., for poles |d_k| |z| > |d_k| and the corresponding x[n] is causal. In contrast, for poles with |d_k| >= 2 --> |z| < |d_k| and the corresponding x[n] is acausal (in the example, this occurs for d_k at z=2). Also, just to clarify, the poles are located at: z=+1/2, +1, +2, along the positive real axis. And remember: A pole cannot be *inside* the ROC by definition. I think the use of "inside" and "outside" the ROC is what's causing confusion here: The way the author is using it here is not meant to mean "inside" the shaded region, but in the sense of |d_k|
This is really helpful.... So you wouldn't need to take into consideration that the constant is actually the higher power there like you would in a normal partial fraction decomposition?
Hi! Thanks for your videos. I had a question. In example two (11:09) , you are given that |z|< 1. But then when you arrive to the final expression you get one of the terms that makes up x[n] to be -delta[n-1]. And this function has a ROC of the whole z-plane but z = 0 (so it would have a pole at z = 0). Then, I don't understand why the final expression for x [n] fulfills that its ROC is |z|< 1, since for this term (the delta function) , its ROC doesn't include z = 0. Thanks a lot!!
Is the ROC in inverse z transform necessarily need to be same as it's original z transform ROC ? If not, how would I choose the right poles for ROC of Inverse Z transform ?
Hi can I ask a question about having a term like this:
A/(1-dk*z^1)^L
If L = 4
would that make the inverse z transform:
A[(n+1)*(n+2)*(n+3)/3!]*dk^n*u[n]
also, would u[n] be a delta function?
Hello! Are you familiar with the term "linear Fractional Transformation?" Could you please tell me about any book or published document using the term "Linear Fractional Transformation?"
I have a video entitled "Inverse of linear ratio (Ax+B) /(Cx+D) is: (-Dx+B) / (Cx-A). Believe it or not but I thought that I was the first person to have discovered this fact but someone sent me the following link where I found my discovery on page 4 of the class assignment. I went to the copyright office and could not find anything with "linear Fractional Transformation" in the title. Thank you!
at 9:40 how does the pole at z=1/2 is inside the ROC. Isn't the ROC in 1
Note that the pole is not located inside the ROC as 1/2
+Barry Van Veen At 9:45, why does the pole at z = -2 give rise to a non-causal z inverse transform, whereas the pole at -z = 1 gives rise to a causal z inverse transform? I thought the system was causal only for values INSIDE the ROC. Also you said in the video that z = 1/2 gives rise to a causal z inverse transform??
I thought the systems was causal for 1
@@jamesduffin3839 I think I see the confusion. The earlier part of the video did suggest what you've said, however, I think that you need to compare the magnitude of z within the ROC: 1 < |z| < 2, with the magnitude of each pole. e.g., for poles |d_k| |z| > |d_k| and the corresponding x[n] is causal. In contrast, for poles with |d_k| >= 2 --> |z| < |d_k| and the corresponding x[n] is acausal (in the example, this occurs for d_k at z=2).
Also, just to clarify, the poles are located at: z=+1/2, +1, +2, along the positive real axis.
And remember: A pole cannot be *inside* the ROC by definition. I think the use of "inside" and "outside" the ROC is what's causing confusion here: The way the author is using it here is not meant to mean "inside" the shaded region, but in the sense of |d_k|
Thank you so much, your explanation is very good🌸
superb! good example for right explanation
A huge video. Thanks.
You would take it into account when you factor the denominator before breaking into the par-frac.
this really help me thanks Mr. Barry :))
This is really helpful.... So you wouldn't need to take into consideration that the constant is actually the higher power there like you would in a normal partial fraction decomposition?
Thank you so much that was really helpful ❤
Thanks a lot! Great video!
Hi! Thanks for your videos.
I had a question. In example two (11:09) , you are given that |z|< 1. But then when you arrive to the final expression you get one of the terms that makes up x[n] to be -delta[n-1]. And this function has a ROC of the whole z-plane but z = 0 (so it would have a pole at z = 0).
Then, I don't understand why the final expression for x [n] fulfills that its ROC is |z|< 1, since for this term (the delta function) , its ROC doesn't include z = 0.
Thanks a lot!!
There is a pole z=-1 and z=2. The pole at z=0 is canceled by the zero at z=0.
Thankyou So Much Buddy... This indeed is top Notch :')
Thank you so much for this tutorial.I have exam after 2 days.:D
Well organised videos. :) No any time losses with writing or drawing. It is so good for me. Thanks a lot. :)
Great
Thank you very much
thank you
Thank you very much sir :)
Superb
Thx
math error, I got the denominator 0 when solving for A2,????
Is the ROC in inverse z transform necessarily need to be same as it's original z transform ROC ? If not, how would I choose the right poles for ROC of Inverse Z transform ?
If I will have a question as z^3-10z^2-4z+4/ 2z^2-2z-4