The adaptive linear combiner with a periodic-impulse reference input as a linear comb filter

Abstract

In this paper we present a particularization of the adaptive linear combiner (ALC) filter structure, that results in a linear time-invariant comb filter suitable for the estimation of periodic signals and repetitive time-locked signals. The ALC is used in its transversal form, and the reference input is a periodic unitary-impulse train signal. When the LMS algorithm is used we show that the structure results in a simple and efficient linear time-invariant comb filter, taking as output the output of the ALC. This comb filter has lobe widths proportional to the μ gain parameter of the LMS algorithm, and the separation between lobes is controlled by the period L of the periodic impulse train. We have also analyzed this filter when applied to estimate repetitive signals time-locked to a stimulus, and we show that the effect of a temporal misalignment in the determination of the stimulus results in a low-pass filtering effect, with cut-off frequency inversely proportional to the dispersion of the impulse estimation. This effect is specially important when the time occurrence of the stimulus is not directly accessible and needs to be estimated from some ‘noise affected’ procedures, as in Electrocardiographic signals. The filter is also shown to be equivalent to a time-sequenced adaptive filter with one weight. Finally, an application to somatosensory evoked potentials estimation is presented.