Fast Change of Windows Properties

One of the tasks in signal analyzing is to use proper time window. There are a lot of windows with completely different properties in time and frequency domain. If we need analyze spectrum of the signal we would like to have high selectivity (narrow main lobe of the window) but because of leakage effect we achieve also high level of sidelobes. On the other hand, if we design FIR filter using time windows we need low level of stop band - the window should have sidelobes as low as possible: then we use a Blackman or a Kaiser window. We would like to propose the polynomial window and the simple method to achieve wide main lobe: squaring the computed time window with proper value of coefficients. Using this method the low order polynomial window has similar properties as Blackman or Dolph-Chebyshev window. The polynomial window can realize different criteria of optimization and has lower cost of computation than its competitors