Loading video...

Video Failed to Load

There was a problem loading this video. This could be due to a temporary network issue or the video might be unavailable.

60 years ago this month, the Fast Fourier Transform was created, a powerful tool for image compression & data analysis. Watch a classic MIT breakdown of FFT, perhaps the most-taught algorithm at the Institute: v/MIT OpenCourseWare

MIT CSAIL

348,422 subscribers

187,602 views • 1 year ago •via X (Twitter)

News & Politics Science & Technology Education

Anya Rossi• Live Now

Private livecam show

7 Comments

Vibe Enhance1 year ago

@MITOCW If you know, you know. And if you don’t, this is your sign to start learning.

TappAlpha1 year ago

Designed to generate daily income while capturing the growth potential of the S&P 500, $TSPY helps unlock new financial opportunities. For important information about the fund visit: #ETFs #Investing #IncomeGeneration

Peter Voss1 year ago

@MITOCW Wow - only 60 years ago?

Andrea Allen1 year ago

@MITOCW It’s unreal watching @danielmartinwin it’s almost scary how accurate it is. I started using his exact entries, That's $160,000 in gains.

Mihalis Tsoukalos1 year ago

@MITOCW Great video! Highly recommended!

Robert Daneel Olivaw1 year ago

@MITOCW Erik? We're both from the same hometown!

David Hendrickson1 year ago

@MITOCW The world is so computer science-centric. AI will take care of that. Without FFTs, there would be NO high-speed internet and No smartphones. Come on, EEs, you have to step up. You will soon be at the top of the Tech hierarchy.

Related Videos

The Fast Fourier Transform is the most important numerical algorithm of our lifetime - Gilbert Strang, MIT

The Fast Fourier Transform is the most important numerical algorithm of our lifetime - Gilbert Strang, MIT

Mathelirium

50,548 views • 5 months ago

This video presents a recent breakthrough called the Sparse Fourier Transform (SFT). This algorithm yields an exponential speed-up over the celebrated Fast Fourier Transform (FFT) when asked to extract a small number of dominant Fourier coefficients.

This video presents a recent breakthrough called the Sparse Fourier Transform (SFT). This algorithm yields an exponential speed-up over the celebrated Fast Fourier Transform (FFT) when asked to extract a small number of dominant Fourier coefficients.

Mathelirium

50,777 views • 5 months ago

A breakdown of the simplest neural network from the late MIT Prof. Patrick Winston during his 6.034 (Artificial Intelligence) course. Clip v/tetsuo //: 👾 & MIT OpenCourseWare

A breakdown of the simplest neural network from the late MIT Prof. Patrick Winston during his 6.034 (Artificial Intelligence) course. Clip v/tetsuo //: 👾 & MIT OpenCourseWare

MIT CSAIL

45,739 views • 4 days ago

A free MIT course breaking down mathematics for computer science & engineering: (v/MIT OpenCourseWare) Here, MIT prof. Tom Leighton, who is also the CEO & co-founder of Akamai, discusses what a proof is (Lesson 1).

A free MIT course breaking down mathematics for computer science & engineering: (v/MIT OpenCourseWare) Here, MIT prof. Tom Leighton, who is also the CEO & co-founder of Akamai, discusses what a proof is (Lesson 1).

MIT CSAIL

57,950 views • 8 months ago

The system. this was a speech given at the NACCP Image award some years ago. very powerful speech.

The system. this was a speech given at the NACCP Image award some years ago. very powerful speech.

Don Salmon

38,580 views • 1 year ago

The Fourier transform runs inside every MRI machine, every audio compressor, every signal processor on earth. JPMorgan pays $350K to engineers who can derive it from scratch. There is one professor alive who explains it the way nobody else can. His name is Gilbert Strang. MIT. The most brilliant mathematical mind of his generation. His textbook sits in over 10 million homes. No other person on earth holds this combination of depth and clarity in one head. He opens with one confession. The Fourier transform is unreasonably effective. It solves problems it was never designed for. The goal is not to compute it. The goal is to understand why it works at all. Then the core idea. A periodic signal breaks into pure sine waves. Each with a frequency, amplitude, and phase. The transform finds all three simultaneously. A complicated signal in time becomes a simple picture in frequency. Then 1807. Fourier invented the transform not for sound but for heat. How does warmth spread through a metal rod? In time the equation is a partial differential equation - hard. In frequency space it becomes ordinary - easy. Transform in, solve it, transform back. Then convolution. Convolution in time equals multiplication in frequency. Filtering a signal, removing noise, compressing audio - all multiplication in frequency space. Without the transform: thousands of computations. With it: a few multiplications. Then the delta function. Zero everywhere except one point where it is infinite. Integral equals one. Every mathematician in 1900 said it was not a function. Dirac used it anyway. It took 40 years to justify what engineers had been doing the whole time. Watch the moment Strang shows that the Fourier transform of a delta function is a constant - every frequency in equal measure. The more concentrated in time, the more spread in frequency. This is the uncertainty principle. Not quantum physics. A theorem about any signal at all. A signal processing engineer I know rewatched this before their first project at Apple. Said it was the first time the Fourier transform felt like a change of coordinates rather than a formula to memorize. Free on YouTube, MIT OpenCourseWare. bookmark this and watch later - after this lecture every sound, every image, and every signal will feel like a sum of sine waves waiting to be separated

The Fourier transform runs inside every MRI machine, every audio compressor, every signal processor on earth. JPMorgan pays $350K to engineers who can derive it from scratch. There is one professor alive who explains it the way nobody else can. His name is Gilbert Strang. MIT. The most brilliant mathematical mind of his generation. His textbook sits in over 10 million homes. No other person on earth holds this combination of depth and clarity in one head. He opens with one confession. The Fourier transform is unreasonably effective. It solves problems it was never designed for. The goal is not to compute it. The goal is to understand why it works at all. Then the core idea. A periodic signal breaks into pure sine waves. Each with a frequency, amplitude, and phase. The transform finds all three simultaneously. A complicated signal in time becomes a simple picture in frequency. Then 1807. Fourier invented the transform not for sound but for heat. How does warmth spread through a metal rod? In time the equation is a partial differential equation - hard. In frequency space it becomes ordinary - easy. Transform in, solve it, transform back. Then convolution. Convolution in time equals multiplication in frequency. Filtering a signal, removing noise, compressing audio - all multiplication in frequency space. Without the transform: thousands of computations. With it: a few multiplications. Then the delta function. Zero everywhere except one point where it is infinite. Integral equals one. Every mathematician in 1900 said it was not a function. Dirac used it anyway. It took 40 years to justify what engineers had been doing the whole time. Watch the moment Strang shows that the Fourier transform of a delta function is a constant - every frequency in equal measure. The more concentrated in time, the more spread in frequency. This is the uncertainty principle. Not quantum physics. A theorem about any signal at all. A signal processing engineer I know rewatched this before their first project at Apple. Said it was the first time the Fourier transform felt like a change of coordinates rather than a formula to memorize. Free on YouTube, MIT OpenCourseWare. bookmark this and watch later - after this lecture every sound, every image, and every signal will feel like a sum of sine waves waiting to be separated

Zyphor

120,380 views • 6 days ago

THE MOST POWERFUL VIDEO I'VE EVER WATCHED! A couple of years ago, a family member sent this to me & it helped to change my life (for the better) If you are addicted to ANYTHING, watch this! 999 Days without drinking, gluten, soda, daily fast-food, etc...

THE MOST POWERFUL VIDEO I'VE EVER WATCHED! A couple of years ago, a family member sent this to me & it helped to change my life (for the better) If you are addicted to ANYTHING, watch this! 999 Days without drinking, gluten, soda, daily fast-food, etc...

Mike Webster

30,135 views • 9 months ago

🚨FLASHBACK Trump at the CDC in 2020: “You know my Uncle was a great -- he was at MIT. He taught at MIT for a record number of years. He was a great super genius, Dr. John Trump. I like this stuff. I really get it. People are surprised that I understand it...Maybe I have a natural ability. Maybe I should've done that instead of running for president.” #TrumpMentalHealth

🚨FLASHBACK Trump at the CDC in 2020: “You know my Uncle was a great -- he was at MIT. He taught at MIT for a record number of years. He was a great super genius, Dr. John Trump. I like this stuff. I really get it. People are surprised that I understand it...Maybe I have a natural ability. Maybe I should've done that instead of running for president.” #TrumpMentalHealth

Republicans against Trump

3,115,501 views • 2 years ago

This is awesome, the open for the 1998 Arkansas at Tennessee game 26! years ago. Absolute classic of a game:

This is awesome, the open for the 1998 Arkansas at Tennessee game 26! years ago. Absolute classic of a game:

Clay Travis

297,021 views • 1 year ago

This is a math class this morning at Massachusetts Institute of Technology (MIT). This is the state of learning and ‘free speech’ at our top universities. It would not be happening without a failure leadership at MIT. Imagine being a student who borrowed $250k to attend MIT or a professor who is trying to do research in this environment.

This is a math class this morning at Massachusetts Institute of Technology (MIT). This is the state of learning and ‘free speech’ at our top universities. It would not be happening without a failure leadership at MIT. Imagine being a student who borrowed $250k to attend MIT or a professor who is trying to do research in this environment.

Bill Ackman

18,866,262 views • 2 years ago

This 1 hour MIT lecture on Time Series Analysis will teach you more about Quantitative Trading than a 2 month internship at Citadel or Two Sigma. Bookmark this & give it 1 hour today, no matter what. It’s the most productive thing you do today. Then read the article below.

This 1 hour MIT lecture on Time Series Analysis will teach you more about Quantitative Trading than a 2 month internship at Citadel or Two Sigma. Bookmark this & give it 1 hour today, no matter what. It’s the most productive thing you do today. Then read the article below.

Roan

47,021 views • 3 months ago

Rediscovering the Heartbeat of IITB - the Infinity Corridor! A 450 meters long passageway, built over 60 years ago, connecting all academic departments of the Institute. Paying a tribute to this iconic monument that binds us together, echoing our spirit & passion for learning.

Rediscovering the Heartbeat of IITB - the Infinity Corridor! A 450 meters long passageway, built over 60 years ago, connecting all academic departments of the Institute. Paying a tribute to this iconic monument that binds us together, echoing our spirit & passion for learning.

IIT Bombay

24,109 views • 2 years ago

60 years ago today The Sound of Music was released. The greatest film musical ever created. The fact I always find astounding is that Rodgers & Hammerstein composed this masterpiece towards the end of their careers. The lyric for Edelweiss was the last Hammerstein ever wrote...

60 years ago today The Sound of Music was released. The greatest film musical ever created. The fact I always find astounding is that Rodgers & Hammerstein composed this masterpiece towards the end of their careers. The lyric for Edelweiss was the last Hammerstein ever wrote...

Elizabeth Sharkey

40,928 views • 1 year ago

This 1 hour MIT lecture on "option price & probability duality" will teach you more about options trading than a 2 month internship at Wall Street hedge fund Bookmark this & watch, no matter what. It’ll be the most productive start for your week. Then read post below.

This 1 hour MIT lecture on "option price & probability duality" will teach you more about options trading than a 2 month internship at Wall Street hedge fund Bookmark this & watch, no matter what. It’ll be the most productive start for your week. Then read post below.

0xDipper

33,753 views • 4 months ago

IN 1999 MIT FILMED A MATH LECTURE THAT QUIETLY BECAME THE FOUNDATION OF EVERY AI MODEL YOU'VE EVER USED AND ALMOST NO ONE WAS TAUGHT TO SEE IT THAT WAY 39 minutes from Gilbert Strang, who taught this at MIT for over 60 years -- the linear algebra course an entire generation of engineers and data scientists grew up on. -> The shift it creates: you stop seeing matrices as boring grids of numbers and start seeing them as the language of space, data, and motion itself. School drilled you to crunch matrices by hand and never told you why. Strang shows you what they actually mean. Every neural net, every embedding, every model you prompt is linear algebra running underneath. The math you skipped is the engine of the thing you use all day. Memorizing the steps was never the skill -> seeing what the numbers do is. This is where it finally clicks. Most people fear linear algebra and move on. The ones who watched this see straight into how AI actually works. Bookmark & Watch it today, this one's a legend ↓

IN 1999 MIT FILMED A MATH LECTURE THAT QUIETLY BECAME THE FOUNDATION OF EVERY AI MODEL YOU'VE EVER USED AND ALMOST NO ONE WAS TAUGHT TO SEE IT THAT WAY 39 minutes from Gilbert Strang, who taught this at MIT for over 60 years -- the linear algebra course an entire generation of engineers and data scientists grew up on. -> The shift it creates: you stop seeing matrices as boring grids of numbers and start seeing them as the language of space, data, and motion itself. School drilled you to crunch matrices by hand and never told you why. Strang shows you what they actually mean. Every neural net, every embedding, every model you prompt is linear algebra running underneath. The math you skipped is the engine of the thing you use all day. Memorizing the steps was never the skill -> seeing what the numbers do is. This is where it finally clicks. Most people fear linear algebra and move on. The ones who watched this see straight into how AI actually works. Bookmark & Watch it today, this one's a legend ↓

slash1s

433,431 views • 2 months ago

Jane Street pays $700K/year for quants who know how to apply probabilities and time series analysis in quant trading. This 1-hour MIT lecture on "Time Series Analysis" gives you the same edge quants get paid $58K/month for. Bookmark & watch today. Then read the article below.

Jane Street pays $700K/year for quants who know how to apply probabilities and time series analysis in quant trading. This 1-hour MIT lecture on "Time Series Analysis" gives you the same edge quants get paid $58K/month for. Bookmark & watch today. Then read the article below.

Movez

22,229 views • 3 months ago

MOULIN ROUGE! was released 25 years ago today. Nicole Kidman wore a diamond necklace in the film that was reportedly worth around $1 million at the time, making it one of the most expensive pieces of jewelry ever created for a movie production.

MOULIN ROUGE! was released 25 years ago today. Nicole Kidman wore a diamond necklace in the film that was reportedly worth around $1 million at the time, making it one of the most expensive pieces of jewelry ever created for a movie production.

cinesthetic.

80,971 views • 3 months ago

This is the knife Karmelo Anthony used to murder Austin Metcalf. I carried this exact knife for at least 5 years, up until maybe a month ago. This is not what most people would consider a “pocket knife”. It’s also NOT a multi-tool type of knife.

This is the knife Karmelo Anthony used to murder Austin Metcalf. I carried this exact knife for at least 5 years, up until maybe a month ago. This is not what most people would consider a “pocket knife”. It’s also NOT a multi-tool type of knife.

Derrick Evans

228,084 views • 2 months ago

Trump: I'm standing here with a much more powerful Iran as of a month ago—not anymore. Right now they are decapitated. But I'm standing here a month ago with a much more powerful Iran than it was at any point during 47 years. We’re getting them at the height of their strength.

Trump: I'm standing here with a much more powerful Iran as of a month ago—not anymore. Right now they are decapitated. But I'm standing here a month ago with a much more powerful Iran than it was at any point during 47 years. We’re getting them at the height of their strength.

Acyn

81,872 views • 4 months ago