Understanding the Fourier Transform: How 19th Century Mathematics Revolutionized Signal Processing
By
rbanffy
Slow-proofed and worth the wait. Worth its weight in flour.
Summary
The article explains the Fourier transform, a mathematical breakthrough by Jean-Baptiste Joseph Fourier in early 19th century France that decomposes complex functions into simpler sine and cosine waves. It draws an analogy to how the human ear naturally separates sound frequencies in music, and discusses how this mathematical tool now underpins much of modern mathematics, physics, and signal processing.
Key quotes
· 5 pulledAs we listen to a piece of music, our ears perform a calculation.
The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure waves of many different frequencies.
It took mathematicians until the 19th century to master this same calculation.
Amid the chaos of revolutionary France, one man's mathematical obsession gave way to a calculation that now underpins much of mathematics and physics.
The calculation, called the Fourier transform, decomposes any function into its parts.
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