The Fourier transform dramatically changes the appearance of a time series. Fourier matrixes show spectral energy as a function of frequency.
Below, the illustration shows a Fourier transform matrix. Indeed, it is the matrix that performs the actual transformation.
The Fourier Matrix: a non-random symmetry
First off, the matrix contains weighting factors, ranging from -1 to +1.
- Red is the minimum value (minus 1)
- White is no weight (value of 0)
- And blue is the maximum value (plus 1)
The colors reveal that the weighting factors have undulations and symmetries.
Remarkably these weighting factors transform 2-D time series data values into 3-D energy packets!
It is with these so called “frequency domain methods”, the founder of Insight Inc became acquainted during his experience on US nuclear submarines (Secret clearance).
Chaos or Symmetry?
Only one thing in the ocean environment is random. And that is the white noise background of the ocean itself. However, everything else has a frequency-specific signature and energy. A kind of ever prevailing beauty and symmetry.
Certainly, entities with such geometry can be detected, tracked, and identified using SONAR or signal processing techniques.
For example, the founder of Insight Inc used spectral analysis and advanced modeling methods to study detailed data sets. He did this within the realm of aerospace engineering (Secret clearance).
To sum up, signal processing identifies patterns by making a clean organized signal.