Z-Transform Pole-Zero Cancellation - Z-Transform Part 1

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Several of the previous videos that discussed the Z-Transform mentioned the phenomena of "pole/zero cancellation". When this happens, the ROC can actually grow larger.

This video works an example that demonstrates this phenomena. We start with a finite-length signal that consists of the sum of two parts. Since the signal is finite-length we know the ROC must be the entire complex plan except for possibly z = 0 or z = inf.

We show how these two parts when added together result in a pole-zero cancellation, and a resulting ROC that is indeed to majority of the complex plane.

The next video in this playlist is:

The previous video in this playlist is:

Course website:

  1. Adam Panagos
  2. Z-transform
  3. Pole–zero Plot
  4. Region of convergence
  5. ROC
  6. Pole-zero cancellation
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Great explanation, and excellent compendium of videos. What use can I give to cancelling poles in the system? The Proakis Manolakis book mentions that one must be very carefull in doing this, since if the zero is very near the pole, then the amplitude of the response will be decreased. How can I interpret this in a real system application?

luja
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At 4:44, what happens if we algebraically rewrite that term into: z/(z-alfa) by multiplying it by z/z? Does that not mean that it also has a zero a z=0? Thanks.

kabascoolr
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Drats! Those darn poles turned my amplifier into an oscillator!

silvermica
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Sorry, I am confused, how could the last equation in the video be correct?

stanleynickels
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Didn’t you mean to write: ROC entire plan expect Z = Alpha ? Instead of Z=0

Raph
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