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Fourier Information

The Fourier Transform

The Fourier Transform

This elegant piece of math produces analyses of the basic frequencies of an entity, typically a sound wave. By analyzing frequency and amplitude over time, we get a precise picture of the entity.

Spectrogram

Spectrogram (click for larger)

And That Is Relevant – How?

If we are sets of waves, then we can use the Fourier Transform to analyze – ourselves. Well, we’ll need to start really simple – one electron, perhaps. or even a photon. But if today’s computers can deconstruct the human genome, within ten years it is not impossible that a simple model could exist.

All waves can be deconstructed into a series of sine waves

The idea behind the FFT (Fast Fourier Transform, an algorithm, or set of rules, for analyzing complex wave functions) is that all waves can be deconstructed into a series of sine waves of varying frequency and amplitude. The sine is the simplest possible wave, one frequency only with no additional components. By examining a series of waves, mapping their frequency and amplitude over time, we can see the inner complexities of a sound wave. And we then have the option to edit and rebuild the wave from scratch. Back in the 1980’s we had software that used the FFT, creating graphs like this:

FFT of Audio Wave

FFT of Audio Wave

We’ve Come A Long Way, Baby

Computer speeds have increased 50-fold over that era, and the mathematics packages for complex calculations has likewise expanded its capabilities. Using a factor of the Planck Clock rate as the maximum sample rate or Nyquist Frequency, we should find bands of information, most likely in the very high frequency ranges – think zettahertz on up that change radically and (initially)unpredictably over time, and other frequency bands that are less active. Mapping the pieces together, we could,for example, determine both the entity’s vector and its – oh wait – you can’t determine it’s position anyway, it is a wave, and does not have a point location.

If you would like more information on the Fourier Transform, its uses and processes, try these:
Here’s what Wikipedia says…
Fourier Transform – Better Explained
and my personal favorite…
The Fourier Transform.com


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