Lecture on the Fast Fourier Transform (FFT)

Introduction

• FFT is described as the most important algorithm of all time.
• Used in various applications like watching videos, radar, sonar, 5G, WiFi, etc.
• Initially discovered while trying to detect covert nuclear weapon tests.
• FFT discovery had potential implications for the nuclear arms race.

Historical Context

Post-WWII Nuclear Concerns

• U.S. dropped atomic bombs on Hiroshima and Nagasaki, changing global dynamics.
• Canada and the U.K. requested a meeting with the U.S. about nuclear weapons.
• The U.S. proposed the Baruch plan to control radioactive materials internationally.
• The Soviets rejected the Baruch plan, leading to the nuclear arms race.

Nuclear Testing

• Extensive testing done in remote areas like the Arctic, South Pacific Islands, and Nevada.
• Tests led to thermonuclear bombs, which were exponentially more powerful than atomic bombs.
• 1954 Bikini Atoll test of a device named Shrimp led to unexpected radioactive fallout.

Public Outcry and Test Ban Efforts

• Public opposition to nuclear testing due to health and environmental concerns.
• 1950s and 1960s efforts to establish a comprehensive test ban.

Detection of Nuclear Tests

Challenges and Solutions

• Detecting atmospheric and underwater tests was straightforward with isotopes and hydrophones.
• Underground tests posed difficulties due to contained radiation and Soviet refusal of onsite inspections.
• Led to only a partial test ban treaty in 1963, banning tests where compliance could be verified.

Seismometer Use

• Scientists tried to use seismometers to detect ground vibrations from tests.
• Needed a reliable method to distinguish between nuclear tests and earthquakes.
• Fourier transforms identified frequency components in seismometer signals.

Fourier Transform Principles

Testing Theory

• Signal decomposition into pure sine waves with specific amplitudes and frequencies.
• Multiplying a signal by a sine wave to determine its frequency components.
• Cosine and sine amplitudes needed to determine phase shifts.

Fast Fourier Transform (FFT) Discovery

• Manual calculation of Discrete Fourier Transform (DFT) was highly inefficient.
• FFT developed to reduce computation time from N^2 to N log N operations.

Historical Impact and Rediscovery

Key Figures

• Richard Garwin and John Tukey key in developing and promoting FFT.
• Historical note on Carl Friedrich Gauss who discovered the DFT and FFT, but his work was forgotten.
• FFT's impact on modern technology and signal processing.

Modern Applications

• FFT used in signal processing, image compression, radar, and WiFi among others.
• Important in detecting nuclear tests and potential other clandestine activities.

Conclusion

• FFT is a crucial algorithm with vast applications and significant historical context.
• Potential greater historical impact if widely adopted earlier.

Resources

• Mention of 80,000 Hours, a resource to help people find impactful careers.
• Emphasis on finding fulfilling careers that make a positive impact on the world.

Useful Links

• 80,000 Hours: Find a fulfilling career