Biology Reference
In-Depth Information
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FIGURE 9-14.
The lower panel presents a plot of the percent variance remaining after the data from the LH
example have been fit to a Fourier component, as in Eq. (9-6). A dominant periodic component with
period of about 230 minutes explains 50.2% of the variance of the data and is shown as a dashed line
in the upper panel along with the original LH data from Figure 9-5.
waves. The physiological waveform can, of course, be described by a
series of many sine and/or cosine waves. However, it requires so many
superimposed sine and/or cosine waves that our ability to interpret
the results may be limited.
Figure 9-15 presents the analogous analysis of the GH example from
Figure 9-6. In this example, a period of 1440 minutes only accounted for
22.9% of the variance; a period of 398 minutes accounted for 12.9%; and
a period of 193 minutes accounted for 6.2%. It is clear this GH data
cannot be adequately described by the sum of a few dominant Fourier
components with periodicities of 193, 398, and 1440 minutes. It is
interesting to note that this is an example of the multiple minima
observed when fitting nonlinear equations which we described in
Chapter 8.
C. Periodic Signal Averaging Methods
Figure 9-16 illustrates an alternate approach to the analysis of the
luteinizing hormone example shown in Figure 9-5. This approach
assumes the physiological signal occurs at a regular interval without
assuming the waveform is a sine or cosine wave. The upper right panel
of Figure 9-16 represents the percent of the variance remaining after an
arbitrary waveform is subtracted from the data as a function of the
period of the waveform. The period describing the most variance within
