Biology Reference
In-Depth Information
FIGURE 11-22.
FFT-NLLS analysis of the noisy stationary cosine wave originally presented in Figure 11-14. In this
instance, the method terminated execution after requiring only a single-component cosine analysis in
which three parameters of periodic rhythms expressed in the data were found: the amplitude, the
period, and the phase (Ampl, Per, and Phase). NLLS was performed by a modified Gauss-Newton
method. The convergence criterion was set to a fractional change in variance of 10
6
. Nonlinear
asymmetric joint confidence limits were calculated at 95% confidence (in which lower and upper
parameter confidence limits are estimated independently; the values reported in brackets; the values
reported following รพ/ are one-half the difference between the estimated upper and lower
confidence limits). The results of this analysis indicate that (1) the estimated oscillatory amplitude is
99.63 0.88 y-axis units (producing a RAE of 0.009, not shown on printout); (2) the estimated
period is 23.997 0.011 hours; and (3) the estimated phase is 0.022 0.065 hours. The
extremely low RAE value is indicative of an extremely well-determined rhythm.
following ratio: in the numerator, the amplitude error (one-half the
difference between the upper and lower 95% amplitude confidence
limits) to, in the denominator, the most probable derived amplitude
magnitude. Theoretically, this metric will range from 0.0 to 1.0; 0.0
indicates a rhythmic component known to infinite precision (i.e., zero
error); 1.0 indicates a rhythm that is not statistically significant (i.e., error
equal to the most probable amplitude magnitude); and intermediate
