Fast Fourier Transforms : an analysis tool for share selection

Abstract

The advent of the modern high-speed digital computer has caused a revolution in the application of the theory of digital signal processing to a variety of problems. Digital signal processing has served to create vitality in fields often overlooked by science. One such field is the application of digital signal processing capabilities to the stock market. In the stock market, words such as period, frequency and phase are common pl ace. These words also form part of the engineer's vocabulary. It therefore appears that a certain degree of congruency between the fields may exist. One specific engineering tool of interest to stock market applications seems to be the Fourier Transform. Fourier Transforms were originally developed as an engineering tool to study repetitious (cyclical) phenomena. The benefit of Fourier Transform is its ability to extract the predominate cycle(s) from a series of data, in this instance an indicator or a security's price. Fourier Transform is based on the principal that any finite, time-ordered set of data can be approximated arbitrarily well by decomposing the data into a set of sine waves. Each sine wave has a specific cycle length, amplitude, and phase relationship to the other sine waves, and the interest lies in the decomposition of the stock data array to a basic function on which a decision can be based regarding the behaviour of the signal. The scope of this dissertation shall be to establish weather Fourier Transforms can be used as a decision tool in the selection of Shares. This dissertation takes the point of view that digital signal processing and the rather profound mathematics that accompany them are fields of study unto themselves and beyond the focus of the dissertation.