Performance evaluation of cascaded rectangular windows in spectral analysis

This paper describes a novel approach to the evaluation of the errors associated with the sampling strategy and the windowing process in digital spectral analysis. The proposed procedure, which is based on the introduction of a general expression for the estimation of input signal spectral components capable of separately pointing out the different sources of error, has been applied to the cascade of any number of rectangular windows in presence of periodic sampling. In addition, the approach has been further developed by assuming that the initial sampling time instant could be randomized, so that each spectral component estimated can be considered as a random variable, described through the classic statistical parameters. These parameters quantify the uncertainty associated with the windowing process considered and the sampling scheme adopted. In this paper, they have been theoretically deduced in a closed form in the case of a cascade of two and three rectangular windows respectively, along with a generalisation to the cascade of any number of elements, and compared with those of the single window in terms of the specific errors due to the sampling and windowing (i.e. resolution, leakage and aliasing). In particular, it has been shown that the cascaded technique can carry out a substantial reduction of the uncertainty associated with the input signal harmonic estimates. The comparison between theoretical findings and simulations is provided, showing a very good agreement.