A class of window functions with nearly minimum sidelobe energy for designing FIR filters

A class of window functions is introduced for designing FIR filters. These window functions are obtained from the rectangular window by using a simple frequency transformation. The frequency transformation contains an adjustable parameter with which the mainlobe width and, correspondingly, the minimum stopband attenuation of the resulting filter can be controlled. The transition bandwidth of the filter can then be controlled by the filter order. Like the well-known Kaiser window, the proposed windows are close approximations to the discrete prolate functions which minimize the sidelobe energy. The FIR filters obtained by using the new window are slightly better than those obtained by using the Kaiser window. The main advantages of the proposed window compared to the Kaiser window are that the new window possesses analytic expressions in both the time and frequency domains and no power series expansions are required in evaluating the window function. Furthermore, it provides a better approximation to the discrete prolate functions