FFT: The 60-Year Old Algorithm Underlying Today’s Tech

Computed tomography, streaming of videos and sending images on the internet would not be possible without the rapid Fourier transform. Commonly called FFT, the IT algorithm designed by researchers from Princeton and IBM University is in almost all electronic devices, according to an entry into the Wiki of engineering and technology history.

Demonstrates for the first time in 1964 by the scholarship holders of the IEEE John Tukey and James W. Cooley, the algorithm breaks down a signal – a series of values ​​over time – and converts it into frequencies. The FFT was 100 times faster than the existing discreet Fourier transform. The DFT also requires more memory than the FFT because it records the intermediate results during treatment.

FFT has become an important tool to manipulate and analyze signals in many areas, including audio treatment, telecommunications, digital broadcasting and image analysis. It helps to filter, compress, eliminate noise and otherwise modify the signals.

The omnipresent IT code of 60 years also has applications in peak technologies today such as AI, quantum IT, autonomous cars and 5G communication systems.

The FFT was commemorated with an important stage of the IEEE during a ceremony held in May at Princeton University.

“The Cooley-Tukey algorithm considerably accelerated the calculation of the DFT,” said the president of the IEEE in 2024, Tom Cochlin, during the ceremony. “The previous methods required many more calculations, making the FFT a revolutionary breakthrough. By taking advantage of algebraic properties and periodicities, the FFT has reduced the number of operations, which makes it particularly feasible for daily tasks, replacing less effective analog methods. “

A new mathematical tool

In 1963, Tukey, professor of mathematics and statistics at Princeton, participated in a meeting of the scientific advisory committee of the American president John F. Kennedy to discuss the means of detecting underground nuclear tests, according to the entry of the ETHW.

Richard Garwin, a physicist and engineer in IBM, also attended this meeting which played a key role in the design of the first hydrogen bomb. He died in May. Read on his fascinating life in Mémoriam this month.

Tukey told Garwin that he was working to speed up the calculation of an existing method – the Fourier transform – which could help detection. His algorithm mathematically converted a signal of his field of origin, such as time or space, into a frequency area.

Garwin recognized its potential and asked IBM to select a mathematical analyst to collaborate with Tukey. This person was Cooley, a member of research staff working on digital analysis and calculation projects.

If the Fourier transformed could be done more quickly, Garwin said, seismometers could be planted in the soil in the countries surrounding the Soviet Union to detect nuclear explosions of atomic bombs tests, because the Soviets would not authorize the tests on site, in the history of Cooley in the history of engineering and Wiki technology. A seismometer measures soil vibrations, which are converted into electrical signals and recorded into seismograms.

To design sensors for underground nuclear trials, “you will have to process all seismic signals, and a large part of the treatment could be carried out by Fourier Transforms,” ​​said Cooley in his oral history. But “the computing power at the time was not sufficient to process all the signals you would need to do it.”

The FFT could calculate the frequency of a seismic sensor and produce images, said Harold S. Stone of the IEE Life during the striking event. He is a researcher and colleague emeritus of image processing at NEC Laboratories America, Princeton, and former IBM researcher.

Tukey and Cooley managed the team that wrote the IT code that demonstrated the power of the FFT.

“The demonstration of Coley-Tukey algorithm has shown that it was 100 times faster,” said Stone. “It was so fast that he could follow the seismic data.”

Sensors using the algorithm have been planted, and they detected nuclear explosions within a radius of 15 kilometers from which they were exploded, according to ETHW input.

“By taking advantage of algebraic properties and periodicities, the FFT has reduced the number of operations, which makes it particularly possible and practically possible for daily tasks, replacing less effective analog methods.” —2024 The president of the ieee Tom coughlin

In 1965, Cooley and Tukey published “an algorithm for the calculation of the complex series of Fourier series”, describing the FFT process. Seminal paper has stimulated the development of digital signal processing technologies.

For his work, Tukey received an American national medal in science in 1973. He also received the 1982 IEEE medal of honor for “contributions to the spectral analysis of random processes and the Fast Fourier transformation algorithm”.

COOLEY, which received the 2002 IEEE KILBY SIGNAL SIGNAL MEDAL for the FFT pioneer, was a leading figure in the field of digital signal processing. Thanks to his involvement with the IEEE digital signal processing committee (now known as the IEE Signal Processing Society), he helped establish terminology and suggested research instructions.

Although he is not one of the inventors, Garwin is recognized for recognizing that algorithm had wider applications, especially in scientific and engineering fields.

“In today’s jargon, Garwin helped the FFT to” become viral “by bringing together Cooley and Tukey,” said Stone.

“Garwin and Tukey asked for better information to warn and warn wars,” added Frank Anscombe, Tukey’s nephew. “The FFT Cooley-Tukey quickly advanced this cause by giving a practical and simplifying solution for corrugated data. Thanks to the FFT, a technological rubicon began to be crossed: analog-nummer machine. ”

A spirit of collaboration between the university world and the industry

Like so many innovations, the FFT has emerged from a collaboration between industry and the academic world, and it should be recognized for this, said the colleague of the IEEE Andrea Goldsmith during the ceremony. She explained that she works regularly with FFT in her research projects. At the time of the event, she was dean of Princeton’s engineering and applied sciences. This month, she started her new post as president of Stony Brook University in New York.

“Taking the ideas we have of basic research in our university laboratories, talking to people in industry and understanding how research problems we are working on can benefit from industry tomorrow or in five years or in 20 years, is incredibly important,” she said. “Some people think that engineering is boring and dry and something only the Nerds do, but there is such beauty and creativity in many innovations that we have developed, and I think the FFT is a perfect example.”

The FFT joins more than 270 other stages of the IEEE. They are more than a successful marker, said Bala S. Prasanna, director of IEEE Life, director of region 1 of the IEEE.

“They testify to human ingenuity, perseverance and the spirit of collaboration,” said Prasanna. “These milestones were more than breakthroughs; They have become catalysts of innovation, allowing progress in a way formerly considered impossible. Everyone guarantees that history behind these innovations is preserved, not only as history but as an inspiration for future generations. ”

Another ceremony took place on June 11 at IBM Watson Research Center.

Step plates recognizing that the FFT is exhibited in the hall of the Princeton Engineering and Sciences Applied School and in the main hall at the entrance to the IBM Research Center.

They read:

“In 1964, a computer program implementing a very effective Fourier analysis algorithm was demonstrated in IBM Research. Developed jointly by Princeton University and IBM collaborators, the Cooley-Tuke Streaming technique. “

Administered by the IEEE History Center and supported by donors, the stage program recognizes exceptional technical developments in the world. The section of JEEE Central Jersey Princeton sponsored the appointment.