Analysis and design of modified window shapes for S-transform to improve time-frequency localization

This paper deals with window design issues for modified S-transform (MST) to improve the performance of time-frequency analysis (TFA). After analyzing the drawbacks of existing window functions, a window design technique is proposed. The technique uses a sigmoid function to control the window width in frequency domain. By proper selection of certain tuning parameters of a sigmoid function, windows with different width profiles can be obtained for multi-component signals. It is also interesting to note that the MST algorithm can be considered as a special case of a generalized method that adds a tunable shaping function to the standard window in frequency domain to meet specific frequency localization needs. The proposed design technique has been validated on a physical vibration test system using signals with different characteristics. The results have demonstrated that the proposed MST algorithm has superior time-frequency localization capabilities over standard ST, as well as other classical TFA methods. Subsequently, the proposed MST algorithm is applied to vibration monitoring of pipes in a water supply process controlled by a diaphragm pump for fault detection purposes.