On asymmetric analysis windows for detection of closely spaced signal components

Discrimination capacity, i.e. the capacity to resolve signal components, is probably one of the most important properties of the analysis windows. For components separated by more than a DFT bin the discrimination capacity is determined by the bandwidth and shape of the window's spectral main lobe and the side lobe fall-off rate. The new classical paper of Harris is a milestone where a plethora of windows is discussed and compared through the aforementioned parameters. However, those parameters fail to describe situations given by components clustered within a DFT bin bandwidth. In those cases the discrimination capacity is almost completely determined by the spectral phase of the analysis window, while the shape of the window's magnitude spectrum has little effect. This paper is devoted to a specific class of asymmetric analysis windows capable of resolving components separated by less than a DFT bin. Those windows have recently been proposed and analytically discussed. However, a number of important properties have not been tackled. Herein, the asymmetric analysis windows are thoroughly described and compared to the classical analysis windows in various aspects. The main benefits of the proposed windows are extended discrimination capacity, robustness against additive noise and simple generation. These properties make them very good candidates for narrow-band spectrum analysis of mechanical systems. Results for some real-world examples are presented, showing the capability of the new windows to resolve closely spaced vibration modes when there is a lack of spectral resolution due to the finite register length.