FIR System Modeling and Identification in the Presence of Noise and with Band-Limited Inputs

System identification, that is, the modeling and identification of a system from knowledge of its input and output signals, is a subject that is of considerable importance in many areas of signal and data processing. Because of the diversity of applications, a number of different methods for system identification with different advantages and disadvantages have been described and used in the literature. In this paper we investigate the performance of three well-known system identification methods based on an FIR (finite impulse response) model of the system. The methods will be referred to in this paper as the least squares analysis (LSA) method, the least mean squares adaptation algorithm (LMS), and the short-time spectral analysis (SSA) procedure. Our particular interest in this paper concerns the performance of these algorithms in the presence of high noise levels and in situations where the input signal may be band-limited. Both white and nonwhite random noise signals as well as speech signals are used as test signals to measure the performance of each of the system identification techniques as a function of the signal-to-noise ratio of the systems output. Quantitative results in terms of an accuracy measure of system identification are presented and a simple analytical model is used to explain the measured results.