Study on Estimation of the Finite-Length Unknown Input Waveform from a Given Input Waveform Response

The information obtained by measuring a system can be regarded as a response given by the Black Box when there is an input. In this study, estimation of the finite-length unknown input waveform from a given input waveform response in a second order damped oscillation system is conducted. The theory is shown and verified with the simulation on MATLAB. While the effectiveness of this theory in the real system is shown by carrying out an experiment. The unknown input waveform form is estimated as followed. The impulse response is estimated from the response waveform of the system. Then, Fourier transformation for the response waveform and the estimation waveform of the impulse response was conducted, and the spectrum of the response wave was decided by the spectrum of the estimated impulse response. Lastly, inverse Fourier transform was conducted to this result. This end result obtained is the estimated waveform of the unknown input waveform. In this experiment, the output waveform of the system was measured with an laser displacement sensor. The result was influenced by the noise, however the input waveform was able to be estimated