Understanding the Z-Plane

This tech talk covers how the z-domain (or the z-plane) relates to the s-domain and the time and frequency domains. It also walks through why the z-plane is a polar plot and how the recursion coefficients are the same as z-domain transfer function coefficients.
- Understanding the Discrete Fourier Transform and the FFT: • Understanding the Disc...
- Understanding the Z-Transform: • Understanding the Z-Tr...
- Discrete Control #6: Z-Plane Warping and the Bilinear Transform: • Discrete control #6: z...
- Applied DSP No. 9: The Z-Domain and Parametric Filter Design by Youngmoo Kim: • Applied DSP No. 9: The...
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[@BrianBDouglas]

Hi everyone, I'll be on and answering questions during the premiere. Feel free to drop any questions or comments here in the meantime and I'll try to get to them before then. Cheers!

[@0SuperTacoMan0]

I just found out about the Tech Talks with Brian and oh my... I've been BINGINGGGG on these videos. I just finished my EE degree and watching all these videos with amazing clear explanations have been doing wonders in bridging the gaps of my undergrad knowledge. Thank you so much for these gems, Brian! You da goat.

[@BraplexDongers]

I really liked the domain map, that was really helpful for seeing how the frequency analysis techniques are connected. Also the z domain animation wrapping around the s domain was crazy. This video was great

[@user-xq6dq7xe5e]

at last you have made a video on z-plane after z- transform and have given a reference/recommendation of another video also. May ALLAAH give you better reward

[@sebastianarmstrong2775]

Thank you Brian for a thought-provoking video. The quirks and physical meaning of each domain (frequency, s, z, discrete frequency) felt like an undervalued topic during my undergrad. I have enjoyed your recent videos on this subject--especially the "map" relating the various domains and your intuitive explanation as to why the z-domain uses polar coordinates. I will be recommending this video to friends who have questions on the z-domain. Looking forward to your next video, and I hope you have a great day.

[@bbhh-ud9zo]

I’m currently studying DSP and this is really helpful. Thank you!

[@theverner]

I know z domain but hearing Brian's voice makes me happy😂 I already graduated from my master's but watching his videos reminds me if control theory lectures which were my fav of all.

[@mikewheeler9011]

Hey that was fantastic, can't wait for the digital controller video, thanks 👍🏼

[@BrianBDouglas]

Thanks! A digital controller video would be a good follow up for this.

[@Gowtham-tb5eg]

Thank you sir, i got clarity on z transform

[@BrianBDouglas]

Great to hear 🙌

[@BCarli1395]

Very helpful, thanks.

[@abhijithas9976]

Thanks, i am looking for this type video , got good clarity,

[@tim110-handle]

yes finally!!

[@hughferguson9142]

How can the Z transform help identify how different frequencies decay in a signal? What can it tell about a signal and how the frequencies change over time? Thank you!

[@PankajSingh-dc2qp]

@ 15:01 *integrator* example is also misleading. Integrator is actually a continuous-time device.... the discrete-time equivalent of integrator is *accumulator* that sums the number of samples... Integrator never takes a discrete-time signal as input, u[k] and gives discrete-time output, y[k] as shown in the video.... it works on continuous-time signals

[@rhythmwinicour3914]

How does mapping from the s-domain to the z-domain affect the frequency response of a digital filter? Specifically near the Nyquist rate

[@dominikz5776]

Plot z,s of the tustin transformation s=(2 (z-1))/((z+1) t_s)

[@PankajSingh-dc2qp]

@ 12:24 impulse response should be discrete not continuous because time domain signal is discrete... that is ZT exists only for discrete-time signals

[@PankajSingh-dc2qp]

z-domain is not discrete... it is continuous

[@BrianBDouglas]

Thanks for the clarification, my explanation is misleading. I should have just explained that the Z-domain is the discrete-time equivalent of the S-plane. But you are right, that the domain itself is continuous.

[@bbhh-ud9zo]

RIGHT! DTFT is continuous, while DFT is discrete.