Impulse Response Determination in the Time Domain-Theory

Two methods are presented for determining the impulse response of an object in the time domain when both the input and output time domain waveforms are specified. Pole extraction features can then be applied to the nonimpulsive portion of the impulse response to determine the singularity expansion method (SEM) parameters of the object. The first method involves synthetic division and is comparatively straightforward. The second technique is a least squares method which is computationally more stable. The effect of measurement errors in the input and output waveforms is evaluated for each method. An investigation is made as to what form of the input minimizes the noise variances in the computation. Finally a generalized least squares technique is presented, which yields a minimum variance unbiased estimate for the impulse response when the noise covariance matrix is known.