Abstract
There is an array of numerical techniques available to estimate the period of circadian and other biological rhythms. Criteria for choosing a method include accuracy of period measurement, resolution of signal embedded in noise or of multiple periodicities, and sensitivity to the presence of weak rhythms and robustness in the presence of stochastic noise. Maximum Entropy Spectral Analysis (MESA) has proven itself excellent in all regards. The MESA algorithm fits an autoregressive model to the data and extracts the spectrum from its coefficients. Entropy in this context refers to “ignorance” of the data and since this is formally maximized, no unwarranted assumptions are made. Computationally, the coefficients are calculated efficiently by solution of the Yule-Walker equations in an iterative algorithm. MESA is compared here to other common techniques. It is normal to remove high frequency noise from time series using digital filters before analysis. The Butterworth filter is demonstrated here and a danger inherent in multiple filtering passes is discussed.
Highlights
Physiological processes in almost all plants and animals have adapted to the cycles in the environment, be they daily, tidal, lunar, synodic lunar monthly or annual [1]
The filter length chosen is consistent with the most amount useful information that is being extracted as each iteration extends the length of the filter. This is used in the Maximum Entropy Spectral Analysis (MESA) software employed in our work, but we commonly set a minimum filter length of about N/4 for biological rhythm analyses to ensure adequate representation of any long period cycles in the presence of noise, which can be considerable
To show the difference between Fourier analysis and MESA in one critical area, it was noted above that the possible estimates that can be computed for period in Fourier analysis is constrained by the fact that these estimates can only be calculated for fixed values that are harmonics based on the length of the time series at hand
Summary
Physiological processes in almost all plants and animals have adapted to the cycles in the environment, be they daily (circadian), tidal, lunar, synodic lunar monthly or annual [1]. The filter length chosen is consistent with the most amount useful information that is being extracted as each iteration extends the length of the filter This is used in the MESA software employed in our work, but we commonly set a minimum filter length of about N/4 for biological rhythm analyses to ensure adequate representation of any long period cycles in the presence of noise, which can be considerable. To show the difference between Fourier analysis and MESA in one critical area, it was noted above that the possible estimates that can be computed for period in Fourier analysis is constrained by the fact that these estimates can only be calculated for fixed values that are harmonics based on the length of the time series at hand. Competing interests The author declares that he has no competing interests
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