CYCLICAL ANALYSIS
Identifying Patterns
Fast Fourier Transform
by Amy Wu
Don't overlook cycles when you're analyzing security prices.
For a long time, Fourier transforms were
used mostly by engineers. Transforms were used to study sound waves, frequency
vibrations, and other repetitive occurrences. Since then, Fourier transforms
have been applied to a number of other diverse fields. Aerospace engineers
use them to study a plane's wing-tip vibrations during flight, while musicians
use them to identify patterns when strumming musical instruments. It was
only a matter of time before someone used Fourier transforms for technical
analysis, specifically, a type of calculation called the fast Fourier
transform (FFT). Jack Hutson and Anthony Warren of STOCKS & COMMODITIES
were early proponents of applying fast Fourier transforms to price movements
in security prices.
FOURIER ANALYSIS
Before delving into FFT, it is important to understand the basic principle
underlying Fourier transforms. Fourier analysis is the process of decomposing
seemingly complex, chaotic data into a sum of sinusoids of different cycle
lengths. Each cycle is a portion of a larger, or fundamental, cycle length.
Developed by Jean Baptiste Fourier in 1807, Fourier analysis proves that
any given waveform can be broken down into a combination of sinewaves of
different amplitude (maximum value), frequency (rate of vibration), and
phase -- the three basic properties of cycles. Each sinusoid is characterized
by these three properties. The period or cycle length of the sinusoid is
calculated by dividing the number of trading days per year (assumed to
be 260) by the frequency. For example, a sinusoid with a frequency of 20
cycles per year has a period of 260/20 or 13 days.
...Continued in the July 2002 issue of Technical Analysis of STOCKS
& COMMODITIES
Excerpted from an article originally published in the July 2002 issue
of Technical Analysis of STOCKS & COMMODITIES magazine. All rights
reserved. © Copyright 2002, Technical Analysis, Inc.
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