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Geometric Representation of Signals
Chris Bore - Watch Now - Duration: 29:31
Hi Chris,
Great way to simplify things. For others interested in resources to help visual signals (and the math), I like this website:
https://www.jezzamon.com/fourier/index.html
and the videos in the series on YouTube (3 blue 1 brown Season 4):
https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6
Brewster
Thank you for this talk. I loved your humor (4 dimensional words). Using the letters as axis is brilliant to decouple our desire to leap ahead.
Using Cuboid-sphere-of-confusion. OMG, the definition of RMS in dimensionality reduction.
"A filter projects onto a lower-dimensional space," So many deep concepts explained so simply.
A fourier transform is a rotation, as is a PCA?! (I come from a data science background)
One thing that I didn't understand throughout it all: I'm used to working in audio... I'm used to thinking of samples in terms of time domain. It hurts my brain a bit to think of each sample being a dimension, and I feel like I'm missing something there.
Does it mean that there exist only one signal in universe with bandwidth B and time constraint T?
I'm not sure I grasped the question but no - bandwidth and time duration alone do not define a unique signal: and indeed both constraints are formally not possible. But even if they weer that would not be unqiue: however, a sgnal defined in both frequency and time would be, in a sense, unique.
I'm expecting Mr. Bill to come marching across your paper and straws. (for those outside of US: reference to old Saturday Night Live shows)
hi. Here is the link to the Comms book (and other stuff ; you can also download the PDF of the book for free how nice) from the italian guys at Lausanne who teach on Coursera also
https://www.sp4comm.org/getit.html
And here is the website for their incredible 'foundations' book - that starts with the geometric perspective (and in my view, is better and easier than the comms book above)
https://fourierandwavelets.org/
amazingly, that book (and a sister book on wavelets) are both on there as free PDFs also. (you just need a free 2 years to study them)
PS Yes, 3b1b is brilliant on youtube - he also presents a section on Khan Academy on multivariate calculus/vector stuff (another amazing free/donatable resource for general maths and sci)