Abstract: A system for determining the modal characteristics of a structure in which a plurality of driving signals which have a common preselected frequency and a preselected set of amplitudes and phases corresponding to the estimated parameters of a mode of interest are applied to the structure. The common preselected frequency is in general a complex frequency. The response of the structure to the driving signals are then sensed. Means are provided for receiving the driving signals and the sensed responses, for generating a set of transfer functions characteristic of the structure corresponding to the mode of interest and for obtaining from such set of transfer functions improved estimates of the complex frequencies and complex residues of the mode of interest, that is the damping, frequency, magnitudes and phases of the mode of interest.

Abstract: A system for determining the location of poles in the complex s-plane and their residues from empirical data is disclosed. The system utilizes the impulse response or similar data of a specimen and through repeated differentiations of a frequency domain representation of this response locates the frequency of the poles. The results of any two consecutive differentiations are used to determine the location of the poles in the s-plane and their residues.

Abstract: A system for determining the transfer function of a specimen from an input or driving signal and an output or response signal. The driving signal and response signal are each divided into segments or frames of data, each frame of equal duration and a sum is formed for each frame of data. A time-domain to frequency-domain transform is taken of the two sums; the transfer function is then determined from the transformed data.