V.1:2 (2628): A MiniGuide to Fourier Spectrum Analysis by ANTHONY WARREN, PH.D./STAFF WRITER
Product Description
A MiniGuide to Fourier Spectrum Analysis
by ANTHONY WARREN, PH.D./STAFF WRITER
The basic idea behind Fourier Analysis of time series is to decompose the data into a sum of sinusoids
of varying cycle length, each cycle being a fraction of a common or fundamental cycle length. (For
example, figure 1 shows a time series consisting of a linear trend and two major cycles, and figure 2
shows the decomposition into component sinusoids.) Originally, cyclic analysis was applied to physical
phenomena to describe the behavior of complex vibrations, as for example, the multiple vibrations
created by plucking a stringed instrument. The analysis of such systems is elegantly described by the
behavior of the longest or fundamental cycle, and the response to the first, second and higher order
harmonics of the fundamental. Later, Fourier and others extended this analysis and showed that any finite
data segment or curve could be approximated arbitrarily well by a series of sinusoids, each of which is
periodic over the data interval. This method is the basis of Fourier Analysis of sampled data (time series)
and of conventional spectrum analysis. (Note: the Fourier approximation of a curve or time series is
periodic, even if the data is not!)
In order to understand Fourier Spectrum Analysis we briefly review the properties of an individual
sinusoid. A sinusoid may be uniquely characterized at any point in time by its amplitude or maximum
value, by its frequency or rate of vibration, and by its phase. (See figure 3.) The period or cycle length of
the sinusoid is the number of trading days per year (assume one year is 260 trading days) divided by the
frequency, i.e. a sinusoid with a frequency of 10 cycles per year has a period of 260 / 10 = 26 days.
Fourier analysis decomposes the data into a sum of sinusoids of appropriate amplitude, frequency, and
phase. Fourier Spectrum analysis is a condensation of this data transform, whereby the amplitude squared
or power in each sinusoid is plotted versus each sinusoid frequency. (Phase information is thus lost in the
spectrum representation of the data.) For example, the amplitude spectrum of the cyclic data in figure 1
consists of two data spikes at appropriate frequencies, as shown in figure 4.
FOR THOSE ORDERING ARTICLES SEPARATELY:
*Note: $2.95$5.95 Articles are in PDF format only. No hard copy of the article(s) will be delivered. During checkout, click the "Download Now" button to immediately receive your article(s) purchase. STOCKS & COMMODITIES magazine is delivered via mail. After paying for your subscription at store.traders.com users can view the S&C Digital Edition in the subscriber's section on Traders.com. Take Control of Your Trading. 
Professional Traders' Starter Kit 
All these items shown below only $299.99! 
5year subscription to Technical Analysis of STOCKS & COMMODITIES, The Traders' magazine. (Shipping outside the US is extra. Washington state addresses require sales tax based on your locale.) 5 year access to S&C Archive 5 year access to S&C Digital Edition5year subscription to Traders.com Advantage. 5year subscription to Working Money. Free book selection. 

Click Here to Order 
