Its #Fouriertransform nicely shows the single handedness of the 4-fold axis; what I honestly did not expect are all those sharp peaks!

Acoustics researchers decompose sound accurately into its three basic components #AcousticAnalysis #SineWaves #FourierTransform https://phys.org/news/2023-07-acoustics-decompose-accurately-basic-components.html

A Crash Course On How MRI Machines work https://hackaday.com/2023/05/11/a-crash-course-on-how-mri-machines-work/ #fouriertransform #MedicalHacks #medical #magnet #coils #mri

RT @stecanossa
So: turns out that a circular aperiodic 2D crystal of hats with diameter 300 hats gives this diffraction pattern, and I remain with more questions than answers... but it's definitely a beauty! #aperiodicmonotile #Fouriertransform

The Fourier transform (FT), explained in one sentence: 🔗 https://blog.revolutionanalytics.com/2014/01/the-fourier-transform-explained-in-one-sentence.html
\[\boxed{\hat{f}(\xi)=\displaystyle\int_{-\infty}^\infty e^{-i2\pi\xi t}f(t)\ \mathrm{d}t}\]
#FourierTransform #FourierSeries #Transform #MathematicalTransform #Signal #SignalProcessing #Frequency #Energy #FourierAnalysis #Series #Analysis

End of year. Time to check which page on The Python Coding Book was the most popular this year.

This tutorial just pipped the home page – Fourier Transforms are popular, it seems…

https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/

#Python #FourierTransform #Programming #Coding

#physics #quantumMechanics #fourierTransform https://youtu.be/W8QZ-yxebFA

"Improving Spectral, Spatial, and Mechanistic Resolution Using Fourier Transform Nonlinear Optics: A Tutorial Review"
ACS Phys. Chem Au 2022
https://doi.org/10.1021/acsphyschemau.2c00051
#openaccess #Fouriertransform #Kineticparameters #Lasers #Nonlinearoptics #Plasmons

There's a lot more to say. If you've found the posts above intriguing and you're interested to find out more about how **any** image can be decomposed and reconstructed from nothing other than sines and cosines…

…and you want to go through a step-by-step tutorial to write the #Python code to create this #Fourier decomposition of images, you can read this article:

Code uses #Numpy and #Matplotlib, of course (@matplotlib)

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#Coding #Programming #FourierTransform

https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/

Now, the fun starts if you have lots of gratings superimposed on each other. The #FourierTransform gives you a pair of dots for each of the components

/9

You can find the parameters of a sinusoidal grating by using the 2D #FourierTransform.

The dots shown contain the amplitude and phase of the grating. Their position from the centre gives the frequency, and their orientation represents the orientation of the grating.

/8

What's an image made of?

There are many correct answers.

But the most fascinating one is: << sines & cosines >>

Read on if you're intrigued, as we see how adding lots of sines and cosines to each other will result in an image as in this video below…

This is a journey through Fourier Transforms in 2D!

[continues in replies…]

/1

#Python #Coding #Programming #Fourier #FourierTransform

Researchers thought this was a bug (Borwein integrals) - YouTube
Beautiful: bringing #convolution, the #sinc function and the #FourierTransform together.
https://www.youtube.com/watch?v=851U557j6HE

…time to get inspiration for some other #FourierOptics #Python tutorials to follow on from this, which remains the most popular post on the blog, by far

https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/

#programming #FourierTransform #coding

My favourite textbook of all time – had been in storage for a while as we did a long, convoluted, house move…

It’s back, safe and sound, nicely weathered and thumbed from all those years of use…

PS: just realised it’s my wife’s copy, not mine. I Want My One Back! (It’s still in a box, somewhere…)

#Python #Fourier #FourierTransform #FourierOptics #programming

Now, if you have lots of gratings superimposed on each other, the #FourierTransform gives you a pair of dots for each of the components

/11

You can find the parameters of a sinusoidal grating by using the 2D #FourierTransform.

The dots shown contain the amplitude and phase of the grating. Their position from the centre gives the frequency, and their orientation represents the orientation of the grating.

/10

When the FBI had too many fingerprints in storage | The mathematics of image compression
https://www.youtube.com/watch?v=fRjFwTbJfes
#digitalsignalprocessing #imageprocessing #FourierTransform #dsp #signalprocessing