Numerical construction of impulse response functions and input signal reconstruction

A new method for input signal reconstruction is presented. This approach utilizes the convolution relationship of inputs and outputs of linear systems. A linear discretization of sampled points was assumed in formulating the discrete convolution integral. Subsequently, the resulting equation was modified via a linear constraint to facilitate solution by the least square method. This improves the conditioning of discrete deconvolution. The method was validated numerically on a single degree of freedom dynamic system. Inputs reconstructed matched the applied input very well for a low noise case. A methodology for multiple inputs and outputs was developed. The single input-multiple output formulation was validated using experimental strain measurements of hammer pulse tests. Pulse areas and peak magnitudes were reconstructed with good accuracy.