An efficientway of obtaining formulas of narrowband FIR digital filters based on sinc sum function

A new approach is put forward for obtaining formulas of narrowband lowpass FIR digital filters(NLFDFs) with linear phase based on sinc sum function. Five NLFDF formulas are deduced as examples with stopband attenuation from 47 dB to 90 dB and corresponding relations between filter order and transition width are given. Filter orders designed using four formulas are at least 8.2% smaller than the ones designed using Kaiser window with same stopband attenuation and same transition width and using the remaining formula even 27% smaller. For the design of filters calculation using Kaiser window is incomparable with the calculation of these formulas because the later is not more difficult than calculation using fixed window. In addition, by the same steps as the examples much more NLFDF formulas can be obtained with different stopband attenuation and good performances.