RESUMO

We propose a simple model of the electrical activity of the heart that reproduces realistic healthy electrocardiogram (ECG) signals. The model consists of two RLC linear oscillators periodically kicked by impulses of the main pacemaker with the frequency rate of a real heart. In the proposed model, one oscillator represents the atria, another represents the ventricles, and an electrical cardiac conduction system is included using a coupling capacitor, which can be either unidirectional or bidirectional. The network of the two capacitively coupled oscillators is periodically kicked by the main pacemaker to introduce the periodic forcing of limit cycles into the system; a time delay is introduced to represent the electrical transport delay from atria to ventricles. In this manner, healthy synthetic ECG signals are obtained by combining the signals of the currents of the oscillators. We show that an analytical solution of the model can be obtained when a single impulse is applied. From this, by the superposition principle, a solution with an impulse train is obtained. Note that analytical treatment is a feature not available in current cardiac oscillator models.

Assuntos

RESUMO

This paper presents a forensic methodology that determines, from among a set of recording places, the probable place where allegedly a disputed digital audio recording was made. The methodology considers that digital audio recordings are noisy signals that have two involved noise components. One component is the multiplicative noise, which is an internal feature on the audio recording that is related to the recording device. The other component is the additive noise, which is an external feature on the audio recording that can be related to the recording place. Therefore, the proposed methodology estimates a likelihood rate that helps to decide which recording place is more plausible to be associated with a disputed audio recording. This likelihood rate is defined as the probability of a finding, supposing that a specific proposition is true, divided by the probability of a finding if an alternative proposition is true. Such probabilities are calculated by performing a statistical comparison through the Kullback-Leibler divergence [1], between the probability distribution function of the additive noise associated to the disputed recording and the probability distribution function of the additive noises associated to a set of audio recordings made on the possible recording places. Then, in order to determine the recording place, the analyst requires a list of possible places where the recording could have been carried out; in these places some reference recordings will be made. In this work, the additive noise is estimated by the Geometric Approach to Spectral Subtraction (GA-SS) filter [2], applied to the noisy audio recording.