Design of FIR filters with exceptional passband and stopband smoothness using a new transitional window

This paper demonstrates that FIR filters with excellent passband and stopband smoothness are obtained when sharp transition edges in the ideal filter are replaced with a spline. Although the filters are developed in the frequency domain, a convergence window is identified in the impulse response and compared to windows of popular FIR filters. Design formulae are provided that include parameters to adjust the magnitude response from having characteristics like the maximally-flat designs of Hermann and Kaiser to one having characteristics like the minimum-sidelobe energy approximations of Kaiser and Saramaki. The impulse response coefficients are more straightforward to obtain than these filter designs, while offering preferable response characteristics in many instances. By means of example, adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs. The filters are particularly suitable for accurate filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but are also useful in other applications requiring very low passband and stopband errors