Understanding the Z-Transform

This intuitive introduction shows the mathematics behind the Z-transform and compares it to its similar cousin, the discrete-time Fourier transform. Mathematically, the Z-transform is straightforward—it’s just a bunch of multiplications and additions, and you’ll learn how to solve an equation for a few different signals. However, understanding how to solve a Z-transform equation isn’t as important as understanding why the math is the way it is. Therefore, the majority of this tech talk discusses what you are actually doing when you take the Z-transform of a signal.

Check out these links to learn more about Z-transform:

Chapters:
00:00 Introduction
01:11 Solving z-transform examples
5:00 Intuition behind the Discrete Time Fourier Transform
11:37 Intuition behind the z-transform
19:18 Related videos

--------------------------------------------------------------------------------------------------------

© 2023 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc.

[nurahmedomar]

In university, we were taught how to do the DFT and Z-transform, but never taught why. And this video explains them in crystal clear. Great Job!

[harrytsai]

OMG! I've been waiting for the series of discrete-time control for nearly 5 years!

[erickappel]

I was blown away by the clearness of the explanation! Looking forward to more!

[diegoperezromero]

This is by far the best video about the dtft and z transform i've ever seen. Very good and very detailed explanation.

[jmanius]

Brian is basically my mentor at this point

[MarkNewmanEducation]

Amazing explanation. Thanks so much for explaining things in a more intuitive way.

[emiliomartineziii]

This was truly amazing! This guy has MIT level brainpower. Like woah, his ability to explain and efficiently articulate this stuff is unreal. This channel will be my saving grace in dsp for sure! Already subscribed too. He's a legend for sure!

[HimanshuSharma-bqu]

bless my soul that i landed on this video. the use of complex domain in dft was a "magic" for me. today i stand near to the oz who does the "magic"

[clarklau]

I learned about DFT and z-transform many years ago, but it wasn't until I watched this video that I truly understood what the 'e' and 'z' in these two transformations actually do.

[franciskimonge]

my guy just made fourier transforms, laplace transorm and z transform all make sense, thank you

[mixguru]

My control systems professor should watch this video.

[terrycrews]

been watching ur vids since 2014
ty so much for this, brian

[BingtheLizard]

I've been able to solve a Fourier Transform in analytical form back at uni, without understanding what it was for.
I've been able to implement a Discrete Fourier Transform algorithm in code to do simple frequency analysis of a signal, without understanding why the algorithm was the way it is.
With your explanation, I think I finally get the "why" of the Discrete Fourier Transform, the way it uses correlation. Thanks for this explanation; I feel like one more thing is clicking into place.

[erickappel]

Excelllent explanation! It is the first time someone made the DFT's relation to finite length input clear to me! Thankyou!!!

[Adhithya]

The most intutive and lucid explanation of DTFT and Z transform I have ever seen 💖

[wellid]

One of the best introductions I have ever watched

[Michael-zeoz]

Your explanations and teachings are awesome. This opens my eyes to so many things, and in just 1 video!. Brain, you have been blessed with an amazing gift. Thank you for sharing this with us.

[PrestonRogersJPL]

This was the best explanation on DTFT I have ever seen! Bravo!

[grxoxl]

Honestly, the best explanation of the DFT I've ever seen)

[stewartcopland]

Correct me if I'm wrong, but based on how you've explained it, the z transform is just a discrete version of the Laplace transform?