Estimation of a transient response from steady-state responses by deconvolution with built-in constraints

Evidence suggests that the steady-state response (SSR) elicited by a periodic train of auditory stimuli can largely be understood as a superposition of transient responses. This study is devoted to the problem of how to estimate that transient response from measured SSRs. The proposed method differs from previous approaches in that the solution can be constrained to be consistent with physiology-based prior knowledge or educated guesses. To achieve this goal, the transient response is not represented by a time series, but by a linear combination of auxiliary functions, called components. Constraints are introduced by assigning certain properties to the components. Only few parameters are required for that purpose, because the individual components are derived from a suitably designed mother component. After adjusting the components to the problem at hand, the component amplitudes are determined by optimizing the match between predicted and measured SSRs. This requires solving a linear inverse problem. A model simulation as well as an analysis of exemplary experimental data (auditory SSRs elicited by periodically presented clicks) prove the workability of the method. Since part of the theory is quite general, it would be relatively easy to refine and extend the method. Not only could responses other than SSRs be dealt with, it could also be realized that certain key parameters of the transient response, such as amplitude and delay, depend on stimulus repetition rate.