Uncertainty Principles and the Fourier Transform

This video discusses how fundamental uncertainty principles, like the Heisenberg uncertainty principle, arise from the Fourier Transform.

These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[masoudsakha]

I am Phd student in control engineering and also interested in theoretical physics. I love how concepts in these areas appear in both fields like the Heisenberg Uncertainty principle. Beautiful description again by Prof. Brunton. Thanks

[sachinr]

Huge Respect for you Sir,
You are literally spoon-feeding many of yours and other high impact research articles which are very hard to understand in the first go.
Thanks a lot for making these amazing lectures, I think, your lectures are going to be so popular like Prof. Gill Strang MIT OCW.

[raghebalghezi]

Thank you so much professor for your indefatigable efforts!

[danielhoven]

Super cool! Just finished reading this chapter in the book, perfect timing!

[prasundatta]

I wish you were my course teacher of signal processing class. Thanks for your awesome efforts.

[jeanpinter]

Excellent video! You explained the Gabor Uncertainty Principles so well. Thank you.

[SRIMANTASANTRA]

Professor Steve, thanks that's nice

[rdurian]

thank you. I'm no way not a mathematician, but that made more sense to me than anybody else's explanations.
seems like such Uncertainty applies in general in the real world whenever you CALCULATE a Z from MEASUREMENTs, x and y.
Cuz there's always a degree of inaccuracy to measurments, so their PRODUCT is the (much worse) inaccuracy of the CALCULATION.
N if you (for fun) hold the CALCULATION accuracy constant, then twiggle one MEASUREMENT's accuracy, the other MEASUREMENT's accuracy has got to
vary
When you measure Time more accurately, you 'gotta' measure Speed less accurately to get a Distance with an accuracy held constant.
Tho I dont know why anybody'd WANT to do that, except to illustrate Uncertainty in everyday terms...

[eyesburning]

Great explanation and really like the teaching setup. Could you please share some information on how to achieve this (background, glass, lighting, slide projection, etc.)? Thank you, Professor!

[dipanjanmech]

Fourier transform is similar to basis transformation in vectors as you mentioned. In that case does it mean that there is always uncertainty while transforming one basis to another basis or one function to another function or the uncertainty only exists for Fourier transform because of the nature of relation between time and frequency?

[ionutlungu]

Please tell me how you draw, how you make these presentations, i am fascinated, looks amazing Mr Brunton.You mirror image?

[hemilfichadia]

Explanation is awesome but how you are able to write in mirror style that is normal for viewers ?

[ondrejmihalik]

3:38 The left-hand side of your equation should be divided by the square of the energy of the function f. Otherwise the principle would be broken by small-amplitude functions such as f(x) = 0.5exp(–t^2).

[abc]

Can't thank you enough .. god bless

[walo]

Are you writing backwards??? Incredible!!

[learnmore_today]

Could you please do a video showing the application of FFT in 2D with implementation of boundary conditions. You've showed us the solution of the heat equation in 1D, I'll be thankful if you can do the same in 2D with B.C. using FFT. Thanks in advance.

[BhaskarChakradhar]

What if the input wave is a pure sine wave, theoretically speaking, we will know the the frequency of the wave at all points right ?

[naoismeister]

Why is it that the product of the two functions of distance and frequency have to be greater than or equal to a constant?

[s.l]

But what is the point of the x squared and w squared in the uncertainty principle inequality? I get squaring the function and integrating it gives you the energy? But the squared variables seem arbitrary.

[xjuhox]

Cool, but if you use nice visuals then you might begin with a *one* sinusoidal wave with a one *frequency*, then two and more as a superposition. The uncertainty principle builds up is a clear fashion.