Invariant delay estimates for systems with periodically-varying delay

In this paper, output expressions of a periodic signal filtered by two different periodically-varying delay functions are obtained by means of Fourier series decomposition. The percentage power in the harmonics corresponding to the input is analyzed. Next, the identification of a single invariant delay is considered; this is useful in situations where an invariant delay is utilized in the system model in place of a time-varying one which is much more difficult to track. Input signals with harmonic suppression are used and results are compared between the cases with and without output harmonic filtering at the suppressed harmonics of the input. Such filtering is a common pre-processing step when periodic signals are applied to estimate linear dynamics in the presence of nonlinear distortion. The bias introduced by harmonic filtering on the estimated value of the delay is analyzed through Monte Carlo simulations.