Harmonic analysis of time-limited signals

Abstract

The problem of the estimation of the harmonic content of a signal is studied. The study is limited to the class of causal signals which are the response of linear stable systems to pulse inputs. Two cases are examined: (i) the output of a system whose model has one real pole; (ii) the output of a system whose model has a complex conjugate pole pair. An analytical expression for the error that arises when using the finite Fourier transform is obtained. It is shown that the method required to deal with these two cases are sufficient to deal also with systems having many zeros and poles. The principal dependence of the error on the observation interval length is discussed, and also its dependence on other parameters, such as the ratio of the input pulse length to the observation interval length, and the position of the poles of the system model in the s-plane.