Fourier youtube videos

Dunckx
Dunckx
Joined: 8 Jan 22
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Topic 226746

Hi Folks,

 

Just joined a couple of days ago.  If you can afford to spend three quarters of an hour, there's two outstanding videos on the Fourier transform and Fourier series on the 3blue1brown channel:


https://www.youtube.com/watch?v=spUNpyF58BY Fourier transform
https://www.youtube.com/watch?v=r6sGWTCMz2k Fourier series

 

I spent many a year doing Fourier transform nuclear magnetic resonance spectroscopy and these two are by far the clearest explanations I have ever seen.

Mike Hewson
Mike Hewson
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Joined: 1 Dec 05
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Welcome to E@H !Yes,

Welcome to E@H !

Yes, Grant Sanderson is an epic presenter of mathematical themes and these videos are no exception.

We make heavy use of Fourier techniques in our searches here, as we seek to identify oscillatory sources so that's a natural match. A key question is over how long a time interval can we coherently integrate ? Sensitivity goes like the square root of that interval, so to double the sensitivity one has to quadruple the time. We use a hierarchical approach where candidates are identified by client machines and they return a list of possible hits for further deeper analysis. This has been exceptionally fruitful in the detection of new pulsar sources in the radio band and also with gamma-ray data. Our achievements and other analyses are under the Science->Discoveries and Science->Publications menu items.

May you be fortunate enough to receive one of the coveted personalized framed discovery certificates ! :-)

I wish I had seen Grant's presentations before I was formally taught the Fourier work.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
Mike Hewson
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Joined: 1 Dec 05
Posts: 6,281
Credit: 150,208,854
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Actually here is a recent

Actually here is a recent publication which outlines the full mathematical glory/gore involved in the search methods at E@H. It is worth emphasising that a great deal of thought goes into the search design and target selection to make the best use of the computing power that E@H represents. Please also note that while we haven't yet found a continuous wave from a neutron star the searches have placed upper limits on parameters that can be modelled ie. is informing the theorists of the constraints on the equation of state for these objects.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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