The adaptive chirplet transform and visual evoked potentials

We propose a new approach based upon the adaptive chirplet transform (ACT) to characterize the time-dependent behavior of the visual evoked potential (VEP) from its initial transient portion (tVEP) to the steady-state portion (ssVEP). This approach employs a matching pursuit (MP) algorithm to estimate the chirplets and then a maximum-likelihood estimation (MLE) algorithm to refine the results. The ACT decomposes signals into Gaussian chirplet basis functions with four adjustable parameters, i.e., time-spread, chirp rate, time-center and frequency-center. In this paper, we show how these four parameters can be used to distinguish between the transient and the steady-state phase of the response. We also show that as few as three chirplets are required to represent a VEP response. Compared to decomposition with Gabor logons, a more compact representation can be achieved by using Gaussian chirplets. Finally, we argue that the adaptive chirplet spectrogram gives a superior visualization of VEP signals´ time-frequency structures when compared to the conventional spectrogram.