On the Identification of Piecewise Constant LTV Systems Using a Double Periodic System Model

Abstract

Identifying linear time-variant (LTV) systems has been of great interest for many decades already and an important problem in many engineering applications. This paper proposes to use a double periodic system approximation for the characterization of LTV radar channels. Hereby, a two-dimensional Fourier series is used to approximate the time-variant transfer function in both time and frequency domain. By observing the system’s response corresponding to an appropriate input signal, this paper presents a mathematical derivation of how to determine the Fourier coefficients. In practice, these Fourier coefficients are often approximated by assuming the LTV system to be piecewise constant in time domain. This paper establishes an analytical relationship between the original Fourier coefficients and the approximated ones and it investigates how the Fourier coefficients get distorted due to this assumption. Further, this paper provides practical measures to evaluate and control the degree of distortion in advance by adjusting the input signal modulation. This is illustrated by simulation results that are carried out for a double periodic system model with fictitious Fourier coefficients. Consequently, it is shown how the provided results are applied to chirp sequence modulated radar systems and how the radar signals can be interpreted from a system-theoretical perspective.