Seeing any Fourier transform showing the relation between physical space (time domain) and wave space (freq doimain) is very cool since I’ve always wanted to better understand XRD as a physical Fourier transform.
Fourier transform of a Square wave
S(ω)= Sin(ωt)+1/3 Sin(3ωt)+1/5 Sin(5ωt)+......
ω is the fundamental frequency, frequency of the first order and the higher order frequency 2ω, 3ω, 4ω are called harmonics.
Fourier transform analysis of square wave contains only odd harmonics order and even orders are zeros.
Figure shows square wave in time domain and Fourier transform of Square wave in frequency domain.
#Fourier_transform#Squar_wave
It amazes me that people do not use suitable wavelet - HAAR ( or db1) to describe a periodic wave that is square. ( two Haar functions back to back ) or my own work in using "Pseudo Wavelets" originated from a "Shape based" transform. It would result in less Harmonics and no "ringing" with a benefit of knowing locations of start and finish of rising pulse such as Haar function. Just a note - there is no such thing as a "clean signal" in both strength or period - all signals in nature "suffer from random noise" be it temperal or volume. As for "trapezoidal" signal Δt - rise will alway approximate a Δt→0 But they will always be be Δt+ε.
This type of Fourier analysis falls apart if the signal is digital communication - there is no such problem in wavelet analysis. Wavelets can differentiate digital signal. And as 3D can differentiate a "shape" using a "pseudo Wavelet" transform from background noise of a rapidly moving radar signature such as a plane or a rocket. My work from (1995-2001) after CSIRO redundancy ( I have to say that as they claim everything just by being there employee at some stage of my life - for instance anything to do with IP and patents I generated at CSIRO )
I did my work in 1996 but I still see this Gibbs type approach in signal analysis. Fourier is best used as algebra tool box in Wavelets.
I liked the graphics... try reconstruction using Wavelets.
Some intro notes ( I need to do more );
https://lnkd.in/gYNpW2ZQ
===>>> What was the secret Wavelet?
Base level was to construct Pseudo-Wavelet based on the Sokolov CAM shape. Filter out the shape and then recognize the location of the "tape" - an induced fault.
===>> How did this fit into existing Wavelet Theory?
1. Yves Meyer produced a continuous Wavelet.
2. Ingrid Daubechies produced first recursive discontinuous Wavelet
3. Pseudo-Wavelet produce effective behaviour filter such as dynamics.
I was in 1996 inspired by Daubechies db4 wavelet and its db1 equivalent to Haar Wavelet. This allowed my construction of a "Shape based" (CAM) Wavelet.
==>What did CSIRO lose?
1. Lead in emergent Wavelet field.
2. Sokolov CAM system as applied to wider industry.
3. CSIRO lost the ownership of the critical part of the fibre processing machine.
===>> Read More https://lnkd.in/g3zVeiG4
==>>>Lesson that CSIRO needed to learn is this; IF YOU HAVE A SUCCESS DO NOT CHANGE THE PEOPLE THAT GOT YOU THERE
#scienceandtechnology#australia#career#TeamCSIRO#science#phd#stemcareers#stemeducation#stem#engineering#csiro#xcsiro
=>>I once had respect for CSIRO now I don't #engineersaustralia
Fourier transform of a Square wave
S(ω)= Sin(ωt)+1/3 Sin(3ωt)+1/5 Sin(5ωt)+......
ω is the fundamental frequency, frequency of the first order and the higher order frequency 2ω, 3ω, 4ω are called harmonics.
Fourier transform analysis of square wave contains only odd harmonics order and even orders are zeros.
Figure shows square wave in time domain and Fourier transform of Square wave in frequency domain.
#Fourier_transform#Squar_wave
https://lnkd.in/e2wFJy-M
In many of the YouTube videos that I’ve shared, it is often mentioned that YOU should gather in groups, as small or as large as you like to expedite the process of earth’s and humans’ ascension to the 5D reality.
But what does that has to do with the video I’m sharing NOW?
The fastest way to ascension is to synchronise our vibration to earth’s new vibration. First you must get someone who CAN “read” earth’s new vibration. BUT nobody knows how, so I’m THINKING if metronomes CAN synchronise itself, it MUST have some logical explanation to it.
Perhaps it is vibrating to earth’s vibration? Just like throwing an object into a calm lake, the wave reverberate outward. Thus, earth vibration starts from the core and vibrate to the surface causing all the surface objects to synchronise.
Therefore, we will all synchronise eventually but some takes longer than others. Reminder - there’s ONLY 32 metronomes in this video but we have approximately 8 billion (lesser after the pandemic but more if inclusive of other NONE HUMANS living on earth).
However, I challenge the idea if my suspicion is correct, if I set up another different set of 32 metronomes, they are all going to synchronise in unison to validate these metronomes are in synchronicity with earth’s vibration all the time. SO?
So, you just vibrate in sync with the metronomes to create the “100 monkeys effect” to expedite the ascension process!
The ability to delay short light pulses suffers from a significant distortion of the delayed pulse - https://lnkd.in/dp4g39ZB
This Letter [#OPG_OL] demonstrates the possibility of all-optically controlling the group delay in a photorefractive crystal to solve the issue. Titled “Zero-broadening slow light from photorefractive two-wave mixing,” the paper presents a technique to slow down shorter or longer signal pulses without distortion.
The technique uses the two-wave mixing (TWM) effect in the pulse regime at room temperature to achieve this.
Written by: Nacera Bouldja, Marc Sciamanna, Alexander Grabar, and Delphine Wolfersberger
#NonlinearOptics#Light#Photorefraction
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8moWow, looking at the waveform simulation, feels like am back in college days doing optical Fourier transforms.