V.17:4 (151-158): The Discrete Fourier Transform Illusion by Dennis Meyers, Ph.D.

V.17:4 (151-158): The Discrete Fourier Transform Illusion by Dennis Meyers, Ph.D.
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TheDiscreteFourier Transform Illusion by Dennis Meyers, Ph.D.

The Fourier transform is a mathematical technique for analyzing data to determine cyclical component. Take a close look.

The Fourier transform is a mathematical technique named after mathematician Jean Baptiste Joseph Fourier(1768-1830).Thatthis technique, devised long before any of the modern amenities that we take for granted today, is widely used today in science and engineering for digital signal processing is a remarkable accomplishment. The application of Fourier mathematical techniques is prevalent in our everyday lives in everything from television to wireless telephones to satellite communications.

STOCKS & COMMODITIES is certainly no stranger to Fourier analysis. Back in 1983, S&C publisher Jack Hutson and Anthony Warren published a number of articles on using the Fourier transform and the fastFouriertransform(FFT) inanalyzingstockprices. (For a primer on the FFT process, see the sidebar, “What is a fast Fourier transform?”)

Here, we will take a different approach and examine how the discrete Fourier transform (DFT) and its modern implementation, the fast Fourier transform (FFT), can be applied to the Standard & Poor’s 500 daily index. I will demonstrate possible misuses of this sophisticated analysis this time, and next time, I will present a method to use this analytical process.

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