Signal to noise ratio analysis of maximum length sequence deconvolution of overlapping evoked potentials

In this study a general formula for the signal to noise ratio (SNR) of the maximum length sequence (MLS) cleconvolution averaging is developed using- the fi-equency domain framework of the generalized continuous loop averaging deconvolution procedure [Ozdamar and Bohorquez, J. Acoust. Soc. Am. 119, 429-438 (2006)]. This formulation takes advantage of the well known equivalency of energies in the time and frequency domains (Parseval's theorem) to show that in MLS deconvultion, SNR increases with the square root of half of the number of stimuli ill tile sweep. This increase is less than that of conventional averaging which is the square root of the number of sweeps averaged. Unlike arbitrary stimulus sequences that can attenuate or amplify phase unlocked noise depending on the frequency characteristics. the MLS deconvolution attenuates noise in all frequencies consistently. Furthermore, MLS and its zero-padded variations present optimal attenuation of noise at all frequencies yet they present a highly jittered stimulus sequence. In real recordings of evoked potentials. the time advantage gained by noise attenuation could be lost by the signal amplitude attenuation due tp neural adaptation at high stimulus rates. (c) 2006 Acoustical Society of America.