FREQUENCY-DOMAIN LEAST-SQUARES SYSTEM-IDENTIFICATION

A frequency domain least-squares (FDLS) parameter-based system identification algorithm is defined in order to identify model parameters from vector spectrum analyser data. The input consists of sines and cosines at known frequencies and the output is the magnitude and phase angle of the response as measured by the spectrum analyser. Cosine, sine and complex exponential formulations each have different and important characteristics: the cosine formulation is found to identify the real part of the system; the sine formulation identifies the imaginary part of the system; and the complex exponential formulation identifies the complete system. However, if group delay is added to the measurements (as is always present in actual spectrum analyser data), the real part of the delayed transfer function contains information from both the rear and the imaginary parts of the original transfer function. Thus, in practice the cosine formulation has been found to perform as well as the complex formulation without the need for complex arithmetic.