Variance of Fourier coefficients calculated from overlapped signal segments for system identification

In frequency domain system identification, the Fourier coefficients and their variances are used to calculate the estimated parameters. They are calculated from the measured signals. Therefore, good estimation of the Fourier coefficients and of their variance is utmost importance. It is a common practice to segment the periodic signal into periods, calculate the Fourier coefficients in each period, average them, and perform variance analysis, too. Here an important questions arises: do we use all the information present in the signal? Can we improve this procedure? This paper analyzes the information utilization in the process, examines when is it optimal, explains when processing of overlapped segments can help and why, and suggests an improved preprocessing procedure, increasing the quality of the calculated Fourier coefficients.