A characterization of a single-trial adaptive filter and its implementation in the frequency domain

A single-trial adaptive filter (SAF) was implemented in the frequency domain (FDAF) by using the Fast Fourier Transform. The FDAF is significantly more efficient than the SAF. In the data presented the FDAF ran approximately 2 times faster than the SAF. For time series containing larger numbers of data points (n) the efficiency of the calculation will increase on the order of N/Ln(N). The FDAF was tested under a variety of conditions to determine the limits of its usefulness. Pre-filtering the data was found to be necessary to prevent the FDAF from lining up on high frequency activity not related to the signal. The importance of minimizing the amount of low frequency noise was emphasized since it adversely affected the performance of the FDAF and was difficult to filter. The single-trial latencies predicted by the FDAF were much more sensitive to increasing noise than the final wave form. In the absence of excessive low frequency noise a negative exponential relationship was found between the mean error in latency prediction and the SNR estimate. Since the SAF technique is also used to determine signal latency in single sweep data the SNR estimate can be a useful test to determine if the FDAF is locating the signal correctly or merely amplifying chance regularities in noisy data.