Spectral Analysis for Circadian Rhythms: A Perspective on Theory, History and Practice

The present study highlights maximum entropy spectral analysis for circadian rhythms. These periodicities are studied in systems ranging from intracellular fluorescence to complex behaviors such as running wheel activity; data acquisition and format vary accordingly. There is an array of numerical techniques available to estimate the period of circadian and other biological rhythms. When selecting a method, one must consider factors such as resilience to stochastic noise, sensitivity to weak rhythms, resolution of numerous periodicities or signals embedded in noise, and accuracy in measuring periods. 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. MESA has proven itself superior to standard Fourier analysis as it does not produce artifacts resulting from the various manipulations needed absent a model for the function. Both resolution and sidelobe suppression are also superior to standard Fourier analysis. 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 the 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.