Fractional Kaiser Window With Application to Finite Impulse Response Digital Filter Design

This study introduces a new adjustable window derived from the recently proposed fractional modified Bessel function of the first kind with zero order. The proposed window, referred to as the fractional Kaiser window in this study, is obtained using the Kaiser approach, which was originally used to develop the well-known Kaiser window, and encompasses the Kaiser window as a special case. First, spectral analysis of the proposed window is conducted across various window lengths to evaluate its spectral performance. The comparative results reveal that the proposed window offers superior ripple ratio values, ranging from 1.67 dB to 5.20 dB, compared to the Kaiser window for the same half-mainlobe width at N = 51. Next, the effectiveness of the proposed window in the design of finite impulse response (FIR) digital filters is assessed. After analyzing the filter’s spectral performance for different values of the independent parameters, a general comparison is made with filters designed using the Kaiser window, demonstrating that superior filters can be achieved with the proposed window. Finally, three design examples of digital filters are provided, with different filter lengths ( $N =51$ , 71, and 101) and filter transition widths, to compare with other windows in the literature. The simulation results indicate that the proposed window consistently produces better filter designs in all three examples by offering the largest minimum stopband attenuation values.