Recent searches
Search options
#fourier
0 posts0 participants0 posts today
Teresita
The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. It decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. This is particularly useful in many fields, such as signal processing, physics, and engineering, because it allows for analysing the frequency characteristics of signals. The Fourier Transform provides a bridge between the time and frequency domains, enabling the analysis and manipulation of signals in more intuitive and computationally efficient ways. The result of applying a Fourier Transform is often represented as a spectrum, showing how much of each frequency is present in the original signal.
\[\Large\boxed{\boxed{\widehat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,\mathrm dx, \quad \forall\xi \in \mathbb{R}.}}\]
Inverse Fourier Transform:
\[\Large\boxed{\boxed{ f(x) = \int_{-\infty}^{\infty} \widehat f(\xi)\ e^{i 2 \pi \xi x}\,\mathrm d\xi,\quad \forall x \in \mathbb R.}}\]
The equation allows us to listen to mp3s today. Digital Music Couldn’t Exist Without the Fourier Transform: http://bit.ly/22kbNfi
Gizmodo · Digital Music Couldn't Exist Without the Fourier TransformThis is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny
ѦਹѤʞ Replied in thread
There's a lot more than can fit in a single thread.
If you want to read more detail, and go through the step-by-step writing of the code to decompose & recostruct *any* image, read full article here:
#coding #2dfourierimages #2dfouriertransform #fourier
/16
The Python Coding Book2D Fourier transform in Python: Create any image using only sine functionsAny image is made up of only sine functions. In this article I'll convince you of this fact by using the 2D Fourier transform in Python
Replied in thread
Now, here’s the “magical” part of #Fourier theory.
Any image is made up of lots of sinusoidal gratings. So, the 2D Fourier Transform of an image gives you thousands of pairs of dots, and each pair represent a sinusoidal grating.
/12
