V.12:4 (146-152): SIDEBAR: WHAT IS A FAST FOURIER TRANSFORM? by Technical Analysis, Inc.

V.12:4 (146-152): SIDEBAR: WHAT IS A FAST FOURIER TRANSFORM? by Technical Analysis, Inc.
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WHAT IS A FAST FOURIER TRANSFORM? by Technical Analysis, Inc.

There is an intuitive appeal in the concept that cycles are apparent in price data. The cycles do not appear to be consistent, but more of a combination that are longer- and shorter-term cycles added together. This creates a market of upward movements with countertrend declines and downward movements with countertrend rallies.

Now look at an ideal example of this process. In sidebar Figure 1, the line labeled A+B+C is a composite or a summation of waves beginning with the trend (labeled C) and the two wave forms labeled A and B. If we just look at one cycle of wave A, we can see that from point 1 to point 64 is one wave. The wave then repeats itself over the next set of data points. If we look at wave B, we can see that this wave repeats itself five times from data point 1 to data point 64. So with respect to our 64-point time period, we can say that wave A has a frequency of one cycle per 64 data points and wave B has a frequency of five cycles per 64 data points. The cycle length is the inverse of frequency. If the data points were days, then wave A's cycle length would be 64 days and wave B's would be 12.8 days (sidebar Figure 2).

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