FREQUENCY-DOMAIN LEAST-SQUARES SYSTEM-IDENTIFICATION

A frequency domain least-squares (FDLS) parameter-based system identif ication algorithm is defined in order to identify model parameters fro m vector spectrum analyser data. The input consists of sines and cosin es at known frequencies and the output is the magnitude and phase angl e of the response as measured by the spectrum analyser. Cosine, sine a nd 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 par t 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 a s the complex formulation without the need for complex arithmetic.