David Dorran - The z-Transform

I'm trying to synthesize finite fields. What I am looking for is a way to use finite differences to approximate (i.e. synthesize) the complex exponential function to just the degree necessary for a given fidelity of representation. See e.g. Finite-difference time-domain method.

The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved.

See e.g. this Unity page: Realtime Global Illumination using Enlighten.

I looked at this video again after seeing Toby: "Locked in a school bus until I learn what fractals are" and thinking about Norman Wildberger - How Physicists do Maths and Modeling Probability Distributions and Solving Differential Equations. 

He has some detailed notes that go along with this series: https://pzdsp.com/docs/ in particular The z-transform: A practical overview.

He has a cute Matlab tool for visualising complex exponentials and negative frequencies:

Here's the full playlist, with some advice for golphers at the end:

Subscribe to David Dorran.

Comments

Post a Comment

Popular posts from this blog

Live Science - Leonardo da Vinci's Ancestry

Image
... and his posterity too? See  On Communication in Linear Time And Hypertext And The Gospel of Sophia . So it looks like El Cielo of the cistine [sic!😂] chapel is not the limit anymore.  I think I just met one of his descendents. A guy called Versailles Toledo who is from Chiapas. That might explain the murals I mention in my recent untitled post , just before the post mentioning this video. I also just took this photo of Rafael Gonzales, born here in Tecate, B.C., who told me about a spring near here called Agua Fría , half way from Tecate to Loma Tova , where, a few decades ago, people used to go to have barbecues and stuff, but now he thinks it may be private land. If someone reading this has a Facebook account, please write a link to this post onto his FB page. To see why I took the photo, look at his T-shirt and the horse-shoes and ponder this: Subscribe to BeatrizER and her video(s?) about mathematical logic, ... Sounds like Edith (II) Rix has been online all the time, ...
Read more

David Turner Obituary by Sarah Nicholas Fri 24 Nov 2023

Image
This was in The Guardian: David Turner obituary , only eight days after I posted  David Turner Talking About Sixty Years of Functional Programming History : This talk was given in London in 2017: See  Turner, D. A. "Some History of Functional Programming Languages" also  John Hughes - Why Functional Programming Matters  and David MacQueen's talk at ICFP 2015 in  Numberphile - Sophie Maclean on the Catalan Numbers . At 10:30 This whole discussion abut combinator reduction is especially interesting. I didn't know Arthur Norman had tried building hardware for combinator machines. I'll look that up: maybe start here A.C. Norman  Faster combinator reduction using stock hardware  in LFP '88: Proceedings of the 1988 ACM conference on LISP and functional programming. At 26:25 on the ISWIM virtual machine implemented in the PAL compacting garbage collector?! This work Reynolds and others did was at MIT in Masecheusetts and Argonne National Laboratory Illinois. Did
Read more