
Show HN: Interactive Essay on Signals, Sampling and the Fourier Transform - jackschaedler
http://jackschaedler.github.io/circles-sines-signals/
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streptomycin
Normally I'd just upvote and move on, but this is really fucking good. For
example, I wish I could have seen something like that "Sine Wave Aliasing"
page when I was learning this stuff, would have saved me a lot of confusion.

~~~
jackschaedler
Thanks! Let me know if there are other topics you'd like covered, or areas
that need more explanation.

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shorodei
Another topic that has confounded me as much as FFTs are Quaternions.

~~~
cbd1984
Take a look at geometric algebra.

[http://www.geometricalgebra.net/](http://www.geometricalgebra.net/)

[http://en.m.wikipedia.org/wiki/Geometric_algebra](http://en.m.wikipedia.org/wiki/Geometric_algebra)

~~~
GFK_of_xmaspast
That's not quite the same, but worth reading up on anyway.

~~~
cbd1984
The quaternions are a subalgebra of geometric algebra. It's not quite the same
in that it's strictly more general and, therefore, more broadly applicable.

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tomek_zemla
This is awesome. Congratulations! It should be thrown in the face of the
textbook publishing industry that still charges $100+ dollars for yearly
reprints of paper bricks.

This is what the textbooks should be in the 21st century! Outstanding work and
hopefully it will inspire new generation of academics to take the outdated
textbook publishing monopolies out of the loop in the future.

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SandB0x
This is one of the best pieces of expository writing I've ever seen. I
particularly love the interactive phasor visualisation here:
[http://jackschaedler.github.io/circles-sines-
signals/dft_int...](http://jackschaedler.github.io/circles-sines-
signals/dft_introduction.html)

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deitcher
I wish they could have done things like this when I was learning signals and
transforms as an undergrad. But interactive didn't really exist in the early
90s.

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gdubs
This is an _incredibly_ well-crafted piece of work. I mean -- my god -- the
pressure wave animation? [1]

1: [http://jackschaedler.github.io/circles-sines-
signals/sound.h...](http://jackschaedler.github.io/circles-sines-
signals/sound.html)

~~~
davyjones
As a side note, the pressure that is waxing and waning in that diagram is very
very small compared to atmospheric pressure.

The actual air molecules are moving at a much higher speed (the root mean
squared velocity is dependent on the temperature). But if we imagine that
these are weightless dust particles suspended in air, the diagram is accurate.

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zwieback
Like!! It took me a while to chew through signals and FT back in school
(before the web) so I really appreciate how this is bringing browser-based
animations to the general public. It's a lot easier to understand that way.

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geographomics
This is a wonderful piece of work. Exceptionally clear writing and excellent
use of interactivity.

One minor bug report, the mathematical pi symbol (U+1D6D1) used in the unit
circle doesn't appear to be displayed correctly (Chrome 40, Windows 7):
[https://i.imgur.com/zt0HDLO.png](https://i.imgur.com/zt0HDLO.png). It's okay
in Firefox though.

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danabramov
Really great. One nitpick: I looked 10 seconds for "Next" link. Would be
better as a single article IMO.

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Pluizer
I registered an account just to say thanks, this is brilliant! Exactly what I
was looking for.

~~~
jackschaedler
Wow, that really means a lot. Thank you! Really glad to hear that you are
finding it useful. Please send along your feedback and questions if anything
doesn't make sense or is poorly communicated in the text/visualizations.

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TheOtherHobbes
This is truly outstanding. I'd love to see an entire series done like this.

Maybe you could Kickstarter this, and use it as a template for a series of
DSP/Electronics/Physics titles?

~~~
tomek_zemla
Absolutely! I would gladly contribute to a Kickstarter fund to pay for your
efforts. I am sure I am not the only one...

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jfoutz
It seems like the equation processing gets messed late in section 4 - $$
\mathrm{DFT}[k] = \sum_{n=0}^{N-1} \mathrm{x}[n] \cdot (cos(\varphi) -
sin(\varphi)i) \\\ where \quad \varphi = k \frac{n}{N} 2\pi $$

[https://jackschaedler.github.io/circles-sines-
signals/dft_wa...](https://jackschaedler.github.io/circles-sines-
signals/dft_walkthrough.html)

there are a few other examples in section 5

Aside from that, this is really great.

~~~
Kronopath
That's because you're accessing the site from HTTPS, or you have HTTPS
Everywhere installed which is doing it for you. I think he's loading MathJax
as HTTP, which means it gets blocked because it's coming from an insecure
connection.

~~~
schoen
Thanks for this observation; I've commented on the existing GitHub issue to
add this information.

[https://github.com/jackschaedler/circles-sines-
signals/issue...](https://github.com/jackschaedler/circles-sines-
signals/issues/6)

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erc11
This is fantastic. I've been looking for something exactly like this to learn
DSP. My brain learns best with kinds of resources. Well done!

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shas3
This is incredible. I wish more professors in universities incorporated this
stuff in their teaching. I occasionally use Wolfram Demonstrations:
[http://demonstrations.wolfram.com/](http://demonstrations.wolfram.com/)

But you take it to another level! Congratulations!

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pdh
Really nicely done. Thanks for sharing!

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CookieMon
Did you use a tool to make the interactive diagrams, or just write all of them
by hand?

(I can imagine myself forever tweaking each diagram, and having to cut back on
them, but you've created them everywhere they might be useful - it's a
fantastic site)

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rbonvall
Hi Jack, awesome work! Did you write the HTML by hand or did you use or write
some static generator? I'd love to have sidenotes like yours automatically
generated and positioned.

~~~
Nzen
I can't speak to how he did it, but it looks like he's just using tables and
line breaks & divs to separate sections. You could easily do that by hand.

Alternately, you could use Bret Victor's technique from "Magic Ink": write a
paragraph followed by a span, typically with absolute positioning.
[http://worrydream.com/#!/MagicInk](http://worrydream.com/#!/MagicInk)

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hashmymustache
Incredibly well crafted site. Blasted my eardrums on the sine wave generator.
I could only hear up to 18kHz now...feel like I'm getting old.

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dankoss
The dynamic visualizations are terrific here, I find that signals problems in
textbooks are hard to understand when they are static. Awesome job!

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JoelHobson
This is the future of textbooks.

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arunabh
Wow !

Me being PG in wireless (electircal engg), this should have been in the
curriculum :)

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cozzyd
Someone should write a digital linear algebra textbook in this style.

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dm8
This is great! Please write interactive articles on similar topics.

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alexdmiller
This is so, so cool. I wish this is what all textbooks were like.

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valerian
Outstanding work, very well written, and very helpful. Thank you

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lynchdt
Nice work, this is great stuff.

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tsenkov
Awesome! Thanks for this.

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Sainth
This is simply beautiful

