Identification of Impulse Response of Linear Systems and Synthesis of System Model†

Abstract

It is a well-known fact that the impulse response completely identifies a linear system. In this investigation the impulse response h(t) is approximated by a set of ortho-normalized damped exponentials satisfying the integral squared error criterion. An analogue computer instrumentation is suggested to evaluate the generalized Fourier coefficients of impulse response. To evaluate these coefficients the time reversal of the orthonormal set is essential. This is achieved on an analogue computer by inserting inverters in series with all integrators. The method Suggested in this investigation directly leads to the synthesis of a system model approximating the system.