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Example sentences for: periodicity
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In this section we demonstrate tools for evaluating (1) periodicity in the circadian range, (2) the strength of a rhythm (if there is one), (3) whether or not the rhythm is a fluke, (4) the period of the rhythm.
Such effects have been observed in the analysis of courtship song as a consequence of the sampling rate; fluctuating values from one point to the next suggest periodicity in the range of the Nyquist frequency; for the song records in question and analysis of the pulse-rate fluctuations, 20-s periods, against a background of 10-s sampling intervals [ 21 ] . It is possible to assess quantitatively how likely a given peak in an autocorrelation can be the result of chance alone.
The relatively large number of complete cycles in the data, however, yield very reliable information about the periodicity; and if there is more than one rhythm, the two periods can more likely be resolved by Fourier-based spectral analysis in the same manner that two wavelengths of light can be resolved into separate lines in a spectroscope [ 60 ] . The relationship between the number of cycles present in the data record and resolution is mathematically equivalent to the gain in spectral resolution with the increase in distance between mirrors in an interferometer [ 60 ] . On the other side of the coin, if a very short series is transformed, information about local conditions in the time domain becomes more precise at the expense of resolution in the frequency domain [the information in the time domain is more precise; but the resolution in the frequency domain is greatly reduced [ 38 ] .
Given that the effect of averaging is to smooth a time series and potentially emphasize rhythmicity, the absence of obvious periodicity in cry b , as shown qualitatively in the bottom left panel in Figure 2, suggests that the antennal
We have adopted a strategy for addressing this complexity based on several criteria as discussed in the companion paper [ 27 ] . The overall approach is somewhat subjective, yet it is systematic and does not rely on an arbitrary decision about periodicity in the data.
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