School Me on Filters

I’ve got a couple stupid simple ones on GitHub but I want to get strong understanding of the theory and math behind deriving them. I’m using the filter tool found here, so I’m hoping to wrap my head around it at some point.

Here is a free book from Analog Devices:

https://www.analog.com/en/education/education-library/scientist_engineers_guide.html

That will get you up and running about digital filtering in general.

Could you be more specific? There are single pole, two, three pole etc. There are real, Butterworth etc. and more.
There are FIR ( finite impulse response ). You typical N element filter.
and IIR ( infinite impluse response ) that makes use of previous outputs.
I have some basic here
https://deltamotion.com/peter/Mathcad/Mathcad - Butterworth NG.pdf

For flight simulators there is also a washout filter which is a high pass filter.
https://deltamotion.com/peter/Mathcad/Mathcad - Butterworth NG.pdf

Do you know Laplace transforms?

toda:
thank you for the reference.

Peter:
I don't know Laplace transforms and I'd like to learn the math like this and, generally, pretty much all the math behind signaling/filter theory. I'm learning on my own under a single-dad-with-a-dog-and-full-time-job schedule, so what I figured to do was just ask the experts instead of spinning my wheels to figuring out *what* to learn.

Thank you both for some starting material.

Peter Nachtwey said:

Could you be more specific?

Click to expand...

I thought on this for a minute and I think what I'm going for here is to take a given signal in a given application (motion, process, etc.) and be able to select from among all maps the best that match the terrain. And then worry about tuning, and so on.

JeremyM, back when I went to school, Laplace transforms were taught in the 3rd semester, 1st semester differential calculus, 2nd semester integral calculus, 3rd semester differential equations, which covered Laplace transforms. Then, later in engineering physics class we used the math we had learned.

Teaching yourself calculus, my not be possible.

Ken,

I'll have to knock off the calculus rust from school, but I did keep my textbooks since I'm not convinced they actually age as fast as curriculum. So generally, I'd be looking at a Calculus I -> III self-course, chapter by chapter, exercise by exercise? Is Kahn Academy worth the money as a supplement or should I look elsewhere?

As far as math software is concerned, Mathematica?

I'm down for it in whatever time I've got.

JeremyM said:

Ken,

I'll have to knock off the calculus rust from school, but I did keep my textbooks since I'm not convinced they actually age as fast as curriculum. So generally, I'd be looking at a Calculus I -> III self-course, chapter by chapter, exercise by exercise? Is Kahn Academy worth the money as a supplement or should I look elsewhere?

As far as math software is concerned, Mathematica?

I'm down for it in whatever time I've got.

Click to expand...

https://control.com/textbook/calculus/introduction-to-calculus/

I think at least the basics of calculus can be reasonably grasped by self-study if you've the mind for it.

Limits are not too bad and I find both derivatives and integrals fairly intuitive in their basic conception once you have grasped limits. They're not obvious by any means, especially the methods of performing them, but that's what the textbook is for.

Differential equations is a whole different beast imo though.

plvlce said:

Differential equations is a whole different beast imo though.

Click to expand...

As I’m finding out.

Peter Nachtwey said:

Could you be more specific? There are single pole, two, three pole etc. There are real, Butterworth etc. and more.
There are FIR ( finite impulse response ). You typical N element filter.
and IIR ( infinite impluse response ) that makes use of previous outputs.
I have some basic here
https://deltamotion.com/peter/Mathcad/Mathcad - Butterworth NG.pdf

For flight simulators there is also a washout filter which is a high pass filter.
https://deltamotion.com/peter/Mathcad/Mathcad - Butterworth NG.pdf

Do you know Laplace transforms?

Click to expand...

Peter, your second link is a duplicate, you have another?

tdoa said:

Here is a free book from Analog Devices:

https://www.analog.com/en/education/education-library/scientist_engineers_guide.html

That will get you up and running about digital filtering in general.

Click to expand...

Thanks for this. I remember a website that actually had the different filter format in a block diagram that was also fairly simple to move into code, but this is a bit more complete.

JeremyM said:

Peter, your second link is a duplicate, you have another?

Click to expand...

Washout filter. These are essentially high pass filters that are used on simulators.
https://en.wikipedia.org/wiki/Washout_filter

As for learning. I am retired and I am still learning.

I always liked Laplace transforms as a simple way to do differential equations using algebra. A PID is

PID(s)=Ki/s+Kp+Kd*s
Dividing by s, integrates
Multiply by s differentiates.
Simple.

That is a lot simpler than the formula you normally see using integrator and derivative symbols.

If I substitute j⍵ for s, where ⍵ is the input frequency, I can plot the frequency response of a Laplace transform in a Bode plot. I use Laplace transforms a lot.

If you can get Mathematica then great. It costs $2.5K the last time I checked. II
wxMaxima is pretty good for free.

Here is an example of how I use wxMaxima to compute the symbolic formula for the P and I gains for a simple velocity system.
https://deltamotion.com/peter/wxMaxima/AutoTuneEquations T0P1.html

I can see I need to update some of my wxMaxima examples that are 12 years old. wxMaxima has made big improvements since then.

Look for tutorials for anything you want to learn and go through the examples.

Learning is a marathon not a sprint. Only high school and college student think of learning as a sprint, AKA cramming for a test.

JeremyM said:

I’ve got a couple stupid simple ones on GitHub but I want to get strong understanding of the theory and math behind deriving them. I’m using the filter tool found here, so I’m hoping to wrap my head around it at some point.

Click to expand...

What for you need filtering? Filtering data on sales graphs? Data filtering in closed loop control? What exactly you want to achieve? Just waste time for learning?

I dare to assume that the purpose of the graphs on page 2 https://deltamotion.com/peter/Mathca...worth NG.pdf is not known to you?

What do you think filtering is?