FOURIER ANALYSIS
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1320 ▶ |
| Object type | Discipline oriented, Methodology or model |
A mathematical technique created by the French mathematician Jean-Baptiste FOURIER that permits to decompose any continuous signal through a combination of various sine waves.
A. FOURIER series is a sum of terms each with a defined amplitude and frequency, i.e. a sum of different sine waves.
This may lead to arbitrary representations as well as to a more or less adequate model of some complex process through the cyclical interferences of sine waves that may — or may not — correspond to different interconnected periodicities.
This method is also known as “Frequency analysis”, “Harmonic analysis” or “Spectral analysis”
K. BOULDING however made the following ironic comment: “… spectral analysis (which) is an elegant way of detecting probably nonexistent cycles and throws no light on the real structures and processes which underlie fluctuations” (1972, p.70).
Indeed, as stated by D. BÖHM and F.D. PEAT: “By means of FOURIER analysis, a particular arbitrary form can be built out of sets of periodic waves, each of which is of a global order”.
… and: “While each simple wave represents a global order, when they are put together they add up to produce a complex local order as well” (1987, p.161-2).
The problem is that either that global or local order is very difficult to explain, or that the given explanation may be baseless. Anyhow, as observed by M. TALBOT, FOURIER transforms are the mathematical analogue of a hologram (1991, p.27).
Unfortunately, due to the resulting controversies about cycles and pseudo-cycles: “… economists seem virtually to have lost interest in the theory of fluctuations” (BOULDING, 1972, 4, p.70).
The subject deserves to be reconsidered, possibly using the WEIERSTRASS renormalization, the deterministic chaos models and the renewal in cycles studies started by K.DE GREENE.