Abstract
Complex first order system (CFOS) is applied to simultaneous estimation of system parameters and input waveform from the observed output waveform. This is based on the following properties; (1) An initial value response of CFOS is same as the impulse response of the same CFOS except a complex multiple factor. (2) Responses of CFOS for arbitrary finite duration input can be considered as the responses for specific initial values, so they are also same as the impulse response except complex multiple factors. (3) There is a one to one correspondance between CFOS and damped oscillating system. The system parameters of CFOS can calculated from the parameters of damped oscillating system and vice versa.
Now suppose damped oscillating waveform is obtained experimentally as the output of unknown second order system. The problem is to estimate the CFOS whose impulse response has most resemble real part to the measured waveform. Once such CFOS is determined, the system parameters of unknown second order system can be calculated. An estimation of corresponding CFOS is done by changing CFOS parameters successively to maximize the correlation between the measured waveform and the impulse response waveform of CFOS.
From the estimated parameters of second order system, the impulse response waveform can be calculated. Then the input waveform can be calculated from the measured output and the estimated impulse response. Results of computer simulation are illustrated.
