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#maths

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Pustam | पुस्तम | পুস্তম🇳🇵

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
#Fourier#FourierTransform#Transform
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Simona Zompì

#WomenHistoryMonth if you love #electronic #music learn about Delia Derbyshire, the godmother of #electronica. In the early ‘60s she created the famous arrangement for the Dr. Who series for the BBC and went on composing many more pieces. At the intersection of #maths and music, she was a pioneer of the music we love dancing on today.
bbc.com/historyofthebbc/100-vo

www.bbc.comDelia DerbyshireFamous for her arrangement of the Doctor Who theme tune, there was far more to Delia Derbyshire's creative activity, both at the BBC and beyond.
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