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#fft

2 posts2 participants1 post today

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: 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
Continued thread

@northernlights @SDF @kentpitman @mdhughes @Contrapunctus
Join as always:
telnet lambda.moo.mud.org 8888
co guest
@join screwtape
Currently me'n Slak hanging out in paradise sushi.

I ran out of characters, but I also want to talk a lot about my experiences implementing a pipelined Winograd #fft using rooms and $things in my own #lispmoo2 codeberg.org/tfw/lispmoo2 and my hopes, dreams, secret plans and resolutions for the new year. Dynamic spatial inheritance plus currying and script-descriptio

Codeberg.orglispmoo2I had a name collision some time previously. This is the jam one, a MOO server built on moonclimb.
Continued thread

Lotta #FFT #dsp replies. Didn't even occur to me this q sounded like that. I don't think it is

Given measured event times

t0 = 00:00
t1 = 01:59
t2 = 02:57
t3 = 04:50
t4 = 08:24
...

a priori: period is roughly 1h and is changing length slowly

Eyeballing this data, I can see that t1->t2 must be one period of 58m. Then I can tell that t0->t1 is a 60 and a 59 and t2->t3 is 57+56. So I know the period is changing 1m/cycle.

Now do it with noisy data, but answer is approximate