Parameters of exponentially damped sinusoids in noise and their application to the analysis of visual evoked potentials

Abstract

The backward prediction and singular value (SV) truncation methods for estimating multiple exponentially damped real sinusoids in noise have been studied. The basic theory and algorithm are outlined, and the effect on the error of computational parameters, such as the sampling window, the sampling rate, the order of the prediction-error filter (PEF) and the truncated point of SV, were studied using simulated data. If the computational parameters are carefully chosen, the estimate of frequency and damping factor of a damped sinusoid is quite accurate (within a certain range of signal to noise (S/N) ratio). We use this method to estimate the parameters of visual evoked potentials (VEP) and then reconstructed them from estimated parameters according to the resonant model. The error between original VEP and the reconstructed waveform is within 5%. This method can be used in the analysis and recognition of various systems.