A Better Way to Think About a Notch Filter | Control Systems in Practice

Check out the other videos in the series:
Part 1 - What Does a Control Engineer Do? • What Control Systems E...
Part 2 - What is Gain Scheduling? • What Is Gain Schedulin...
Part 3 - What is Feedforward Control? • What Is Feedforward Co...
Part 4 - Why Time Delay Matters • Why Time Delay Matters...
This video describes an intuitive way to approach notch filter design by thinking about the problem as an inverted, lightly damped, second-order low-pass filter. Then, two additional poles are added to the resulting transfer function to make it realizable and to allow control over the width of the notch. This approach provides a little insight into how each of the terms in the transfer function contribute to the overall shape and location of the notch filter.
Additional Resources:
- Varying Notch Filter with MATLAB: bit.ly/2RnJ1bZ
- Configure Notch Filter Dynamics with Control System Designer in MATLAB: bit.ly/2RlkpAI
- Tuning a Digital Motion Control System: bit.ly/35A8g3m
- Getting Started with Control System Designer: bit.ly/35Fz7L4
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[@BrianBDouglas]

Well, I've tried to not make any mistakes in this video but at least one slipped by. At 10:35, I meant to divide by Wn^2 and not Wn. The way I did it added in additional gain into the system which is why at 10:54 the Bode plot magnitude plot is biased up to 20 dB.

[@prasadelumalai946]

This explanation is awesome...! 😍

[@CanadaElon]

Reciprocate the transfer function and serial two low-pass filters with two symmetric cutoff frequencies around the undamped natural frequency, what a great way.

[@arthurgrunwald3859]

Hi Brian, I just stumbled upon your video of the notch filter. Your explanation is just brilliant! I have been teaching control theory for a long time but this is the clearest presentation I have ever seen. The use of Matlab control design brings it totally alive. Instead of students using the DSP toolbox to design a notch filter without understanding the logic behind it, they should look at your video. Two thumbs up!

[@davidberggren499]

Thank you Douglas! I like how you explain and make the subject clear to us.

[@JacopoT]

Thank for this video and, please, keep them coming!

[@Ensign_Cthulhu]

As an unlettered amateur in this context who has done a little bit of self-teaching on filters, transfer functions and their pole-zero plots, I found I could understand what was going on in the mathematical sense. The next question my mind asks is "Okay, so how does that translate into hardware? What does it look like to start with, w.r.t. component specs, and what am I physically doing to my basic low-pass filter to flip the function and add the poles?" Can you please point me to something that deals with this?

[@kwinvdv]

I prefer to also write the denominator in terms of natural frequency and damping coefficient. The attenuation at the natural frequency of the notch filter then simply becomes the damping coefficient in the numerator divided by the damping coefficient in the denominator (assuming both use the same natural frequency).

[@ramiz856]

I am play guitar as a hobby. I have a Stratocaster whose coils generate a Hum. Thanks to your video I was able to eliminate it. Thank you so much.

[@merden102]

Thanks for great videos.

[@howrobotics2052]

I've just successfully implemented a geometric tracking controller on parrot mambo. Thank a notch added in the correct place, the controller works very fine on a real parrot mambo.

[@TomChrist1976]

Great video !

[@ernstuzhansky]

Many thanks for explanations.

[@MayhemJames]

Brian, I'm seeing a problem: whenever I use "a" to adjust the width, there's a limit. The ratio cannot be less than 1 or the width starts widening again. Try it in Matlab. Set a = 2, a =1, a = 0.1. In fact, if you use a = 2, and then a = 0.5, they're right on top of each other because they're reciprocals. So, how can we get around this?

[@bkpnit1942k2]

Sir, Nice video on Notch filter, can we have video on how to design plant transfer function having rigid and flexible modes of frequency and then designing a notch filter to reject the flexible mode frequency

[@laurencamila9024]

thank you Brian I owe you all I know

[@tempusFugit1337]

Hi, i had a question. If i'm getting things right you derive a Notch filter from a Band stop filter. Is it also possible to derive a kind of "Inverse Notch filter" from a Band Pass filter in the same way ? Greetings

[@BoxingDayAC]

Not in the same way. You can derive a Notch filter by 1 - Band Pass, which is subtracting the input to the Band Pass filter from its output. This is achieved in-circuit with a Difference amplifier using the original signal and the Band Pass output. The circuit varies whether the Band Pass inverts the phase or not since the amplifier can invert it back.

[@kosiumemmuo1804]

how can we get the code you used for matlab

[@Debraj1978]

Inverse of a notch filter is a digitally realizable oscillator.

[@deasename5839]

OK I get it! Good job!⚡☻⚡

[@zeinaali-3569]

Great

[@kosttavmalhotra5899]

😄😄😄😄

[@michelepinato1158]

Great video!