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Geometric Representation of Signals

Chris Bore- Watch Now - Duration: 29:31

Representing signals as geometric vectors is a simple and fundamental basis of signal processing. Outlined by Shannon in the same paper that introduced Sampling Theory, it offers powerful and intuitive ways to think about and analyze signal processing, but is often neglected in favour of the numerical technique that implement its methods. In this talk Chris Bore revisits this interesting topic and its relationship especially with Fourier Transforms, filters and communications.
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JulesP
Score: 0 | 8 months ago | no reply

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)

Brewster
Score: 0 | 8 months ago | no reply

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

Darkphibre
Score: 1 | 8 months ago | no reply

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.

Navneet
Score: 1 | 8 months ago | 1 reply

Does it mean that there exist only one signal in universe with bandwidth B and time constraint T?

ChrisBoreSpeaker
Score: 0 | 8 months ago | no reply

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.
Brewster
Score: 0 | 8 months ago | no reply

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)