Identification of dynamic acoustic systems by orthogonal expansion of time-variant impulse responses

We present a system identification method for dynamic acoustic systems. The system is excited by a periodic sequence the autocorrelation function of which is an impulse train. The circularly shifted versions of such sequence form an orthogonal basis for the corresponding vector space. As each orthogonal component of the system is sequentially excited, the output sample is the expansion coefficient of the instantaneous impulse response. Unfortunately, the expansion coefficients obtained from the output signal are undersampled, and thus, the time-varying impulse response cannot be fully determined. In this study, we estimate the missing expansion coefficients by interpolation. As a result, a full set of impulse responses is obtained that describes the history of the dynamic system. The performance of the proposed method is demonstrated by simulations and real measurements.