Modeling and Identification of Symmetric Noncausal Impulse Responses

Spectrally equivalent causal (SEC) models for single-input/single-output noncausal systems are derived with the objective of estimating the noncausal impulse response. Attention is restricted to symmetric, noncausal impulse responses and the measurements of the system output are assumed to be noisy. It is shown that by using structured SEC models, either state-space or ARMA-plus-noise, consistent estimate of the noncausal impulse response can be obtained by exploiting only the second-order statistics of the measurements. A new version of the correlation techique particularly suited to structured models is presented and analyzed.