Consider a single-degree-of-freedom (SDOF) system subjected to base excitation.
There are certain cases where the response of a system is known, but the base input acceleration is unknown. An example would be a seismic sensor which behaved as an SDOF system. The seismometer data would give the acceleration of the mass. A calculation would then be needed to determine the base input which drove the mass to the measured response. This calculation process is a form of deconvolution.
I have written a paper:
A Digital Recursive Filtering Method for Calculating the Base Input for a Measured Response Acceleration
The paper is posted at: DRFR_base_accel.pdf
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A similar paper is:
A Digital Recursive Filtering Method for Calculating the Applied Force for a Measured Response Acceleration
Posted at: DRFR_applied_force.pdf
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– Tom Irvine