Discover how sounds, images, signals, and electromagnetic waves can be assembled from simple rotating rhythms.
A complicated sound or image can look impossible to describe. Fourier's idea is that it may be built from simple waves.
He proposes that complicated temperature patterns can be represented as sums of sines and cosines.
Mathematicians clarify when and why wave sums converge.
Fourier analysis becomes central to radio, audio, imaging, compression, communications, and quantum mechanics.
Adjust two sine waves. The white curve is simply their heights added together at every moment.
A square wave has sudden jumps. Add odd harmonics and smooth sine waves cooperate to imitate those sharp edges.
The ripples near each jump do not disappear completely; this is the Gibbs phenomenon.
The waveform shows how a signal changes over time. The spectrum shows which frequencies are hiding inside it.
Each rotating circle contributes one frequency. Chain the circles together and the final point traces a richer waveform.
An electromagnetic wave contains an electric field and a magnetic field oscillating at right angles while the wave travels forward.
Once a signal is separated into frequencies, we can filter it, transmit it, compress it, compare it, or reconstruct it.
Equalizers and codecs work by measuring and changing frequency content.
JPEG compression keeps visually important frequency patterns and discards less noticeable detail.
Information is placed onto carrier waves and recovered by separating frequencies and phases.
MRI measurements are converted from frequency information into spatial images.
The symbol is only the doorway. The real exhibit is the connection it reveals.
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