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Given in the absence of external perturbation to the human cardiovascular system, measures of cardiac function, such as heart rate, vary with time in normal physiology. The primary source of the variation is constant regulation by a complex control system which modulates cardiac function through the autonomic nervous system. Here, the authors present methods of characterizing the statistical properties of the underlying processes that result in variations in ECG R-wave event times within the framework of an integrate-and-fire model. The authors first present techniques for characterizing the noise processes that result in heart rate variability even in the absence of autonomic input. A relationship is derived that relates the spectrum of R-R intervals to the spectrum of the underlying noise process. They then develop a technique for the characterization of the dynamic nature of autonomically related variability resulting from exogenous inputs, such as respiratory-related modulation. A method is presented for the estimation of the transfer function that relates the respiratory-related input to the variations in R-wave event times. The result is a very direct analysis of autonomic control of heart rate variability through noninvasive measures, which provides a method for assessing autonomic function in normal and pathological states.