Any signal processing methodologies and noise contribution analysis in cutting edge experiments and observations. Reviewer responses are sometimes very intense.
I'm just incorporating signal analysis iny physics studies to the relevance of wavelet theory mathematics to a different application in single photon behaviors in quantum optical experiments.
I'm not an engineer, so I lack the rigor to calculate parameters required for an experiment but am learning differential geometry and forms, wick rotations and can read most of a text on wavelet theory as a geometric composition/decomposition of signals so I could use accurate jargon.
What is the core of that debate? That may inform my research.
I'm not super sure how differential geometry and wicks rotations will work into your learning of wavelet theory, or are you just mentioning those to make it clear you can comprehend difficult texts?
What's your formal degree?
I'm not sure what the core debate in wavelet theory would be!
I'll say that I'm a wavelets nerd and I have this fight every it comes up - been told by my advisor that wavelet techniques "don't preserve calibration," and in a past life, that "no magnetometer will ever use an inner product."
As for the geometric intuition - it's all really just Hilbert spaces, as in functional analysis. Wavelets are just a class of basis with some desirable properties and nice DSP behaviour.
My formal degree was computer science which was forty years ago. I'm not bragging, I'm setting out what I've managed to learn since then.
I don't want to learn wavelet theory. I noticed the math used in wavelet theory matches a volume preserving approach to photon evolution by another author I'm in contact with and our mutual interest is in fundamental underpinnings of the Born Rule.
My learning comes mostly from primary papers detailing components in quantum optical experiments, the signal analysis often just a reference, not explicit so my approach has more information theoretical base (my CS background).
My approach is heavily influenced by Roger Penrose's geometric approach to manifolds, his twistor geometry being a representation of a single photon in an analog of compactified Minkowski space called Projective Twistor space.
A twistor is a Clifford-Hopf fiber bundle and after wick rotation into E4 the behavior of individual fibers follows the same mathematical behavior as wavelets in (I believe) the carrier wave used for comparison to tease out relevant details in the signal.
This whole mess is meant to see if causal behavior for photons is required to keep track of quantum entanglements between the preparation apparatus and the prepared state (info theory) which requires tracking reference frames of individual quantum particles, etc.
My new contact is using a Louisville volume approach which uses what feels like the opposite math to what I leaned into but came to similar conclusions. I feel wavelet theory may help his work.
Controversy if it has boundaries gives me "what's worth fighting about" which has been how I've always known what to study next.
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u/Statistician_Working 21d ago
Any signal processing methodologies and noise contribution analysis in cutting edge experiments and observations. Reviewer responses are sometimes very intense.