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What Is the Fourier Transform?

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Re: What Is the Fourier Transform?

#181

Post by abdullahkhalids »

kragen wrote: post #103
abdullahkhalids wrote: post #88

Earlier quoted context omitted.

The question is why "so many real-world systems are governed by differential equations" and "so many real-world systems involve periodic motion". Well, stable systems are can either be stationary or oscillatory. If the world didn't contain so many stable systems, or equivalently if the laws of physics didn't allow so, then likely life would not have existed. All life is complex chemical structures, and they require s…

Differential equations aren't limited to describing stable systems, though, and there are chaotic systems that are also in some sense stable. Ordinary differential equations can describe any system with a finite number of state variables that change continuously (as opposed to instantaneously jumping from one state to another without going through states in between) and as a function of the system's current state (as…

I agree broadly with what you say. I didn't have time to make a more comprehensive comment.

Re: What Is the Fourier Transform?

#182

Post by srean »

zozbot234 wrote: post #127
anyfoo wrote: post #33

If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform). This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.

The so-called "Z transform" for discrete sequences is really just a misnomer for the actual method of generating functions (and formal power-series/Laurent-series). You just write a discrete sequence as a power series in z^(-1).

> really just a misnomer

No. Things acquire different names if they are independently discovered by different communities.

Native Americans called Indians. Lol! what was that.

Re: What Is the Fourier Transform?

#183

Post by srean »

im3w1l wrote: post #105
abdullahkhalids wrote: post #88

Earlier quoted context omitted.

The question is why "so many real-world systems are governed by differential equations" and "so many real-world systems involve periodic motion". Well, stable systems are can either be stationary or oscillatory. If the world didn't contain so many stable systems, or equivalently if the laws of physics didn't allow so, then likely life would not have existed. All life is complex chemical structures, and they require s…

> Well, stable systems are can either be stationary or oscillatory. In practice this is probably true, but I can see another possibility. The system could follow a trajectory that bounces around endlessly in some box without ever repeating or escaping the box.

If this box was of a bounded size then that trajectory would have interesting property - there are chunks of time you can edit out such that what remains will look as if they are converging on a point.

I suspect you will find ergodicity interesting.

Re: What Is the Fourier Transform?

#184

Post by anentropic »

Shadowmist wrote: post #134
armanj wrote: post #75

Earlier quoted context omitted.

Years ago, I often struggled to choose between Amazon products with high ratings from a few reviews and those with slightly lower ratings but a large volume of reviews. I used the Laplace Rule of Succession to code a browser extension to calculate Laplacian scores for products, helping to make better decisions by balancing high ratings with low review counts. https://greasyfork.org/en/scripts/443773-amazon-ranking-la…

I always assume that all the ratings are fake when there is a low count of ratings since it is easy for the seller to place a bunch of game orders when they are starting out.

A bigger problem I find is many Amazon listings having a large number of genuine positive reviews, but for a completely different product than the one currently for sale.

Recently I was buying a chromecast dongle thing and one of the listings had some kind of "Amazon recommends" badge on it, from the platform. It had hundreds of 5 start reviews, but if you read them they were all for a jar of guava jam from Mexico.

I'm baffled why Amazon permits and even seemingly endorses this kind of rating farming

Re: What Is the Fourier Transform?

#185

Post by [deleted] »

anentropic wrote: post #184
Shadowmist wrote: post #134

Earlier quoted context omitted.

I always assume that all the ratings are fake when there is a low count of ratings since it is easy for the seller to place a bunch of game orders when they are starting out.

A bigger problem I find is many Amazon listings having a large number of genuine positive reviews, but for a completely different product than the one currently for sale. Recently I was buying a chromecast dongle thing and one of the listings had some kind of "Amazon recommends" badge on it, from the platform. It had hundreds of 5 start reviews, but if you read them they were all for a jar of guava jam from Mexico. I…

[deleted]

Re: What Is the Fourier Transform?

#186

Post by armanj »

kragen wrote: post #102
armanj wrote: post #75

Earlier quoted context omitted.

Years ago, I often struggled to choose between Amazon products with high ratings from a few reviews and those with slightly lower ratings but a large volume of reviews. I used the Laplace Rule of Succession to code a browser extension to calculate Laplacian scores for products, helping to make better decisions by balancing high ratings with low review counts. https://greasyfork.org/en/scripts/443773-amazon-ranking-la…

While this is a good idea, I think it's unrelated to the Laplace transform except that they're named after the same dude?

I referenced 3B1B for the name: youtube.com/watch?v=8idr1WZ1A7Q

Re: What Is the Fourier Transform?

#187

Post by mkipper »

segfault99 wrote: post #69
anyfoo wrote: post #33

If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform). This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.

When I did EE, didn't have access to any kind of computer algebra system. Have 'fond' memories of taking Laplace transform transfer functions and converting to z-transform form. Expand and then re-group and factor. Used a lot of pencil, eraser and line printer fanfold paper for doing the very basic but very tedious algebra. Youngsters today don't know how lucky.. (ties onion to belt, etc., etc.)

Was this professionally or in school? I still did this in an EE program 15 years ago and I can't imagine things have changed since then. I think kids still have to do lots of ugly math in EE classes.

Re: What Is the Fourier Transform?

#188

Post by ajkjk »

adamnemecek wrote: post #82
ajkjk wrote: post #67

Earlier quoted context omitted.

Nah it's on you to be coherent, there's nothing interesting to ask about

You got confused before we even started so maybe you are not the target audience.

If you can't communicate clearly there's no reason to try to take you seriously.

Re: What Is the Fourier Transform?

#190

Post by kragen »

kragen wrote: post #152
jcgrillo wrote: post #143

Earlier quoted context omitted.

One amazing application of spectral theory I always harp on when this topic comes up is Chebfun[1]. Trefethen's Spectral Methods in Matlab is also wonderful. [1] http://www.chebfun.org/

I haven't read it! Thanks for the recommendation!

Apparently he uploaded it to ResearchGate: https://www.researchgate.net/profile/Hector-Carmenate/post/H...
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