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Thread: Fourier Transform

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    Default Fourier Transform

    Now this is cool, and has a vector slant. Not sure its our next file format, but that did cross my mind.

    https://youtu.be/r6sGWTCMz2k

    Steve
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    Quote Originally Posted by mixedgas View Post
    Now this is cool, and has a vector slant. Not sure its our next file format, but that did cross my mind.

    https://youtu.be/r6sGWTCMz2k

    Steve
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    I hated Fourier Transforms in college... but not as much as Laplace Transforms.

    But I did find it intriguing that you could use them to take any curve and create an equation for it... although it might be a mile long.

    I wish I was more interested at the time because I would love to be a master of them now.

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    I remember being fascinated with Fourier transforms back in high school- at that time, I never dreamed that I would eventually figure out how to employ Fourier techniques to process digital audio signals in multiple ways.

    What really stumps me is the Fast Fourier Transform, a unique product of the computer age- a bit of binary voodoo...

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    ... I've used Laplace transforms in my diploma thesis for high speed "averaging equipotential surfaces" (3D-EM-field calculations for particle-acelerator-developments) with "highly parallel" computing (searching/estimating/simulating best formfactor Transputer-grids for up to 128x128 Transputers on one or more ATW's).

    And much later (on a single PC) for fastest possible calculation of "heating values" with different pipeline gas sources (natural or artificial mixtures of up to 10 hydrocarbon gases, hydrogen, N2 and CO2) for the development of special TLD-sensors for Siemens (was canceled, as Siemens "rationalized away" the sub-division we're working with then).

    But could be interesting to dive deeper into Fourier transforms too!

    Viktor
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    Quote Originally Posted by VDX View Post
    ... I've used Laplace transforms in my diploma thesis for high speed "averaging equipotential surfaces" (3D-EM-field calculations for particle-acelerator-developments) with "highly parallel" computing (searching/estimating/simulating best formfactor Transputer-grids for up to 128x128 Transputers on one or more ATW's).

    And much later (on a single PC) for fastest possible calculation of "heating values" with different pipeline gas surfaces (natural or artificial mixtures of up to 10 hydrocarbon gases, hydrogen, N2 and CO2) for the development of special TLD-sensors for Siemens (was canceled, as Siemens "rationalized away" the sub-division we're working with then).

    But could be interesting to dive deeper into Fourier transforms too!

    Viktor
    As I was taking Laplace transforms in school I was thinking "I am never going to use this stuff." My first job out of college was with a team writing DSP based modem software which required knowing how to use Laplace transforms.

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    ... my use of the Laplace transforms was not for super-complex formulas, but more for "net-averaging", where with every point of the simulated area the EM-field value was averaged with the neighbours (and use of some "magic" overrelaxation values), until the differenciation was below the "interest-noise".

    The complete solution of our benchmark took some hours with a common PC with mathematical coprocessor (12MHz clock-speed) vs. 2s with a Cray-XMP (then, 1988, one of the fastest super-computer for 3 Mio$) ... or 2,2s with my "simulated" transputer-grid (for 0,1Mio$)

    Sometimes the basic idea can give super simple solutions, if you find the right entry

    Viktor
    Last edited by VDX; 05-05-2021 at 20:46.
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    Wow, I should have paid more attention to my continuous/discrete signals class in college.

    Would this allow more complex output/faster scanning from the same old galvos?

    Also, the video mentioned using .svg files to generate images. One benefit I see is it seems like this would be a good way for artistically challenged people (like me) to create cool images from .svg files that you can get anywhere on the web.

    Very cool video thanks for sharing it.


    Eric
    Eric in New Orleans

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    Quote Originally Posted by mixedgas View Post
    Now this is cool, and has a vector slant. Not sure its our next file format, but that did cross my mind.

    https://youtu.be/r6sGWTCMz2k

    Steve
    One of the best visualizations of the Fourier Series and transformations I've seen, thanks Steve. Never got into them, though, they made my brain hurt. But like the few others that responded to this post, I did barely learn the 1st and 2nd order Laplace transforms for LRC circuit designing or modeling analog circuit frequency responses for critically damped, under and or over-damped response curves.

    It is conceivable that future generations of the Raspberry Pi (Blueberry Pi, Cherry Pi or Pecan Pi) processor will bring into play Fast Fourier Transforms and give open-loop galvos the ability via "corrected waveform drive signals" to draw accurate shapes that our closed-loop galvos do today. (We don't need no stinkin' closed-loops)
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    I love Laplace transforms for quickly solving differential equations. I mean what else can convert a second order to an algebra problem. Then you just take the inverse. Granted a lot of limit voodoo but it works.I use it for solving ficks diffusion equations first and second while avoiding the erf function route.

    I have not used Fourier transforms yet but am exploring picking off the backplane diffraction pattern from an optical microscope to deconvolute it digitally. The result should avoid many of the issues that blur optical microscopes. Combine that with Z sensing and a confocal pinhole and I might get something spectacular or kill myself while trying to make it work! I doubt I will actually attempt this but I sure would like to.

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