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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