#josephfourier — Public Fediverse posts
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John Tukey the Fast Fourier Transform (FFT) inventor, who coined both "bit" and "software" died exactly 26 years ago today.
The Fast Fourier Transform (FFT), one of the most important algorithms in signal processing and data analysis, was introduced by Tukey & Cooley in 1965.
In 1805, Gauss - studying the orbits of asteroids Pallas and Juno - came up with a method to interpolate their trajectories from discrete samples. What he came up with was mathematically very close to the modern FFT but Gauss never published that work, and didn’t analyze its computational complexity. It predated even Fourier’s 1822 work on heat diffusion - but without the framing or generalization that Cooley & Tukey would bring 160 years later.
In 1965, Cooley & Tukey published their now-famous algorithm that reduced the cost of computing a Discrete Fourier Transform from 𝑂(𝑛²) to 𝑂(𝑛 log𝑛). This leap made real-time signal processing and digital media compression feasible.
From radio telescopes to JPEGs, from audio codecs to quantum mechanics - the FFT is everywhere. It’s one of the most important (and elegant) algorithms of the 20th century - rooted in the genius of Gauss, but brought to life in the computer age.
#JohnTukey #FastFourierTransform #FFT #SignalProcessing #ComputerScience #Mathematics #Algorithm #DataScience #DigitalSignalProcessing #FourierTransform #ComputationalScience #ScientificComputing #HistoryOfScience #Innovation #CarlFriedrichGauss #JosephFourier #JamesCooley #STEM #Engineering #ArtificialIntelligence #MachineLearning #QuantumComputing #ImageProcessing #AudioProcessing #Statistics #TechHistory #Computing #Science #InnovationLegacy #OnThisDay
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John Tukey the Fast Fourier Transform (FFT) inventor, who coined both "bit" and "software" died exactly 26 years ago today.
The Fast Fourier Transform (FFT), one of the most important algorithms in signal processing and data analysis, was introduced by Tukey & Cooley in 1965.
In 1805, Gauss - studying the orbits of asteroids Pallas and Juno - came up with a method to interpolate their trajectories from discrete samples. What he came up with was mathematically very close to the modern FFT but Gauss never published that work, and didn’t analyze its computational complexity. It predated even Fourier’s 1822 work on heat diffusion - but without the framing or generalization that Cooley & Tukey would bring 160 years later.
In 1965, Cooley & Tukey published their now-famous algorithm that reduced the cost of computing a Discrete Fourier Transform from 𝑂(𝑛²) to 𝑂(𝑛 log𝑛). This leap made real-time signal processing and digital media compression feasible.
From radio telescopes to JPEGs, from audio codecs to quantum mechanics - the FFT is everywhere. It’s one of the most important (and elegant) algorithms of the 20th century - rooted in the genius of Gauss, but brought to life in the computer age.
#JohnTukey #FastFourierTransform #FFT #SignalProcessing #ComputerScience #Mathematics #Algorithm #DataScience #DigitalSignalProcessing #FourierTransform #ComputationalScience #ScientificComputing #HistoryOfScience #Innovation #CarlFriedrichGauss #JosephFourier #JamesCooley #STEM #Engineering #ArtificialIntelligence #MachineLearning #QuantumComputing #ImageProcessing #AudioProcessing #Statistics #TechHistory #Computing #Science #InnovationLegacy #OnThisDay
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John Tukey the Fast Fourier Transform (FFT) inventor, who coined both "bit" and "software" died exactly 26 years ago today.
The Fast Fourier Transform (FFT), one of the most important algorithms in signal processing and data analysis, was introduced by Tukey & Cooley in 1965.
In 1805, Gauss - studying the orbits of asteroids Pallas and Juno - came up with a method to interpolate their trajectories from discrete samples. What he came up with was mathematically very close to the modern FFT but Gauss never published that work, and didn’t analyze its computational complexity. It predated even Fourier’s 1822 work on heat diffusion - but without the framing or generalization that Cooley & Tukey would bring 160 years later.
In 1965, Cooley & Tukey published their now-famous algorithm that reduced the cost of computing a Discrete Fourier Transform from 𝑂(𝑛²) to 𝑂(𝑛 log𝑛). This leap made real-time signal processing and digital media compression feasible.
From radio telescopes to JPEGs, from audio codecs to quantum mechanics - the FFT is everywhere. It’s one of the most important (and elegant) algorithms of the 20th century - rooted in the genius of Gauss, but brought to life in the computer age.
#JohnTukey #FastFourierTransform #FFT #SignalProcessing #ComputerScience #Mathematics #Algorithm #DataScience #DigitalSignalProcessing #FourierTransform #ComputationalScience #ScientificComputing #HistoryOfScience #Innovation #CarlFriedrichGauss #JosephFourier #JamesCooley #STEM #Engineering #ArtificialIntelligence #MachineLearning #QuantumComputing #ImageProcessing #AudioProcessing #Statistics #TechHistory #Computing #Science #InnovationLegacy #OnThisDay
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John Tukey the Fast Fourier Transform (FFT) inventor, who coined both "bit" and "software" died exactly 26 years ago today.
The Fast Fourier Transform (FFT), one of the most important algorithms in signal processing and data analysis, was introduced by Tukey & Cooley in 1965.
In 1805, Gauss - studying the orbits of asteroids Pallas and Juno - came up with a method to interpolate their trajectories from discrete samples. What he came up with was mathematically very close to the modern FFT but Gauss never published that work, and didn’t analyze its computational complexity. It predated even Fourier’s 1822 work on heat diffusion - but without the framing or generalization that Cooley & Tukey would bring 160 years later.
In 1965, Cooley & Tukey published their now-famous algorithm that reduced the cost of computing a Discrete Fourier Transform from 𝑂(𝑛²) to 𝑂(𝑛 log𝑛). This leap made real-time signal processing and digital media compression feasible.
From radio telescopes to JPEGs, from audio codecs to quantum mechanics - the FFT is everywhere. It’s one of the most important (and elegant) algorithms of the 20th century - rooted in the genius of Gauss, but brought to life in the computer age.
#JohnTukey #FastFourierTransform #FFT #SignalProcessing #ComputerScience #Mathematics #Algorithm #DataScience #DigitalSignalProcessing #FourierTransform #ComputationalScience #ScientificComputing #HistoryOfScience #Innovation #CarlFriedrichGauss #JosephFourier #JamesCooley #STEM #Engineering #ArtificialIntelligence #MachineLearning #QuantumComputing #ImageProcessing #AudioProcessing #Statistics #TechHistory #Computing #Science #InnovationLegacy #OnThisDay
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John Tukey the Fast Fourier Transform (FFT) inventor, who coined both "bit" and "software" died exactly 26 years ago today.
The Fast Fourier Transform (FFT), one of the most important algorithms in signal processing and data analysis, was introduced by Tukey & Cooley in 1965.
In 1805, Gauss - studying the orbits of asteroids Pallas and Juno - came up with a method to interpolate their trajectories from discrete samples. What he came up with was mathematically very close to the modern FFT but Gauss never published that work, and didn’t analyze its computational complexity. It predated even Fourier’s 1822 work on heat diffusion - but without the framing or generalization that Cooley & Tukey would bring 160 years later.
In 1965, Cooley & Tukey published their now-famous algorithm that reduced the cost of computing a Discrete Fourier Transform from 𝑂(𝑛²) to 𝑂(𝑛 log𝑛). This leap made real-time signal processing and digital media compression feasible.
From radio telescopes to JPEGs, from audio codecs to quantum mechanics - the FFT is everywhere. It’s one of the most important (and elegant) algorithms of the 20th century - rooted in the genius of Gauss, but brought to life in the computer age.
#JohnTukey #FastFourierTransform #FFT #SignalProcessing #ComputerScience #Mathematics #Algorithm #DataScience #DigitalSignalProcessing #FourierTransform #ComputationalScience #ScientificComputing #HistoryOfScience #Innovation #CarlFriedrichGauss #JosephFourier #JamesCooley #STEM #Engineering #ArtificialIntelligence #MachineLearning #QuantumComputing #ImageProcessing #AudioProcessing #Statistics #TechHistory #Computing #Science #InnovationLegacy #OnThisDay
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What Is the Fourier Transform? - Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform?
[Shal... - https://hackaday.com/2025/09/12/what-is-the-fourier-transform/ #discretefouriertransform #fastfouriertransform #digitalaudiohacks #fouriertransform #softwarehacks #josephfourier -
What Is the Fourier Transform? - Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform?
[Shal... - https://hackaday.com/2025/09/12/what-is-the-fourier-transform/ #discretefouriertransform #fastfouriertransform #digitalaudiohacks #fouriertransform #softwarehacks #josephfourier -
What Is the Fourier Transform? - Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform?
[Shal... - https://hackaday.com/2025/09/12/what-is-the-fourier-transform/ #discretefouriertransform #fastfouriertransform #digitalaudiohacks #fouriertransform #softwarehacks #josephfourier -
What Is the Fourier Transform? - Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform?
[Shal... - https://hackaday.com/2025/09/12/what-is-the-fourier-transform/ #discretefouriertransform #fastfouriertransform #digitalaudiohacks #fouriertransform #softwarehacks #josephfourier -
What Is the Fourier Transform? - Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform?
[Shal... - https://hackaday.com/2025/09/12/what-is-the-fourier-transform/ #discretefouriertransform #fastfouriertransform #digitalaudiohacks #fouriertransform #softwarehacks #josephfourier -
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
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
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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
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
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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
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
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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
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
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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
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
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Understanding climate change & its causes goes back almost 2 centuries.
#JosephFourier
1824: Earth’s warmth > sunlight’s affect
1837: atmospheric heat retention is changeable#EuniceNewtonFoote
1856: atmospheric heat retention caused by moisture/CO2-levels#ArvidHögbom
1890s: historic CO2 amts#SPierpontLandry
1890s: selective absorbers#AvanteArrhenius
1896: 5-6°C rise if 2x CO2#JsHansen
1988: NASA, testimonyhttps://daily.jstor.org/how-19th-century-scientists-predicted-global-warming/
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Understanding climate change & its causes goes back almost 2 centuries.
#JosephFourier
1824: Earth’s warmth > sunlight’s affect
1837: atmospheric heat retention is changeable#EuniceNewtonFoote
1856: atmospheric heat retention caused by moisture/CO2-levels#ArvidHögbom
1890s: historic CO2 amts#SPierpontLandry
1890s: selective absorbers#AvanteArrhenius
1896: 5-6°C rise if 2x CO2#JsHansen
1988: NASA, testimonyhttps://daily.jstor.org/how-19th-century-scientists-predicted-global-warming/
-
Understanding climate change & its causes goes back almost 2 centuries.
#JosephFourier
1824: Earth’s warmth > sunlight’s affect
1837: atmospheric heat retention is changeable#EuniceNewtonFoote
1856: atmospheric heat retention caused by moisture/CO2-levels#ArvidHögbom
1890s: historic CO2 amts#SPierpontLandry
1890s: selective absorbers#AvanteArrhenius
1896: 5-6°C rise if 2x CO2#JsHansen
1988: NASA, testimonyhttps://daily.jstor.org/how-19th-century-scientists-predicted-global-warming/
