search

camzmac / bispectrum-visualizer

0 stars 0 forks source link

Another inspiration #1

Open Joshuaalbert opened 4 years ago

Joshuaalbert commented 4 years ago

Hi there,

I saw your blog post explaining that you'd like to build a bispectrum visualiser (As Canadian I use -iser instead of -izer). I think your project is cool. I'm a radio astronomer and we use the bispectrum in a very intuitive way. Technically, the interferometric visibilities that we measure are the bispectrum (I think). We define the interferometric visibilities as,

V(x, y) = <E(x) E^*(y)>

That is the temporal average of the product between the electric field at two different points in space (note the complex conjugation). We typically call this the electric field coherence. Often what people do is write the electric field as the 3D Fourier transform of it's spectrum, 

E(x) = F_s [ \tilde{E}(s)](x)

The purpose of the temporal average is so that the cross-product of Fourier modes of incoherent light will cancel. In which case V(x,y) is simpler to work with. A special case that is often used is that when there is negligable diffraction and the light mostly comes from one direction (not from everywhere on the celestial sphere), then the visibilities can be written as a 2D Fourier transform of another field. This is the Wiener-Khinchin theorem. This other field is the 2D power spectrum of the electric field! So the bipsectrum in a special case is the Fourier of the powerspectrum! It's only when all cross frequency terms cancel so that the bispectrum itself is diagonal.

I'll follow this project and let me know when you have a working visualiser for audio! It would be great to make it a small service with a little web-server for short audio clips.

Joshuaalbert commented 4 years ago

Ah, sorry V(x,y) is not the bispectrum in radio astronomy. It's formed from V as V(x,y) V(y,z)/V(x,z).

camzmac commented 1 year ago

Hey there @Joshuaalbert , thanks for posting to this project, I really didn't see it until today!

Thanks also for your perspective on the use of the bispectrum in radio astronomy 📡

That is a great idea to make it a small web-based service to process audio clips and plot the bispectrum. It would certainly more accessible to the average (interested) person, as well as faster than the hardware project I originally proposed in that blog post. This might make for a good pivot... 👌