A generalized lag window for spectrum estimation with some studies by using simulation

The spectral density function (sdf) is one of the most important tools that is frequently used in practical applications, especially engineering ones. Since the proposal of this function after the middle of the last century and the scientific modifications that were made to it later, many researchers have been interested in the sdf from both its theoretical and applied points of view. One of the most important terms of the sdf is the lag window function, as many lag window functions have been proposed based on various philosophical and practical foundations by well-known researchers in this aspect of scientific work. In this research, a new lag window function will be presented based on a scientific-philosophical analysis of two of the most famous lag windows, which are the Parzen and Bartlett lag windows and the commonalities between them. A simulation study will also be conducted to highlight the theoretical aspect and its practical value. The results showed that the proposed lag window performs excellently when estimating the spectral density function, superior to its counterparts under comparison.