Chirp analyzer for estimating amplitude and latency of steady-state auditory envelope following responses

The envelope following response (EFR) is a scalp-recorded evoked potential elicited by carrier tones or noise, modulated in amplitude with a continuous sweep of modulation frequencies. This non-stationary response reflects the phase-locked neural activity of the auditory pathway to the temporal envelope of sounds and has been commonly assessed by fixed-frequency methods based on the discrete Fourier transform, such as the Fourier Analyzer (FA). In this work, we study the estimation of the EFR with the use of explicit time-frequency methods, which offer more information about the energy distribution of the recorded signal, such as the Short-Term Fourier Transform (STFT) and the Morlet Continuous Wavelet Transform (CWT). We further introduce the Chirp Analyzer (CA), which is similar to FA, but using as basis function the same linear chirp that amplitude-modulates the carrier stimulus. In a direct comparison using controlled simulated responses, the CA showed to be able to estimate the correct EFR amplitudes, without the typical bias offered by the estimation using STFT (equivalent to FA) and more robust to noise than the CWT method, although with higher sensitivity to the presence of a delay in the response with respect to the stimulus. For addressing the latter issue, we also propose here a novel methodology for estimating the apparent latency of the response. This method proved to be reliable when using the STFT and the CA methods, as assessed using simulated responses. The estimation of the EFR amplitude with any of the methods, but especially with CA, should be corrected by using the estimated delay when possible. An illustrative application of these methods to small datasets of a rat and a human newborn, suggested that all time-frequency methods can be used to study the EFR amplitudes in a wide range of modulation frequencies, but they should be interpreted in the light of the limitations shown in the simulation studies.