A Group of Arithmetically Symmetrical Band-Pass Filter Functions

A group of band-pass filter characteristic functions is described which do not have attenuation peaks inside the range 0 < < , hence, correspond loosely to polynomial low-pass filters. The functions might or might not have finite attenuation peaks outside this range. These functions can be made to exhibit arithmetic symmetry in a limited band by adjusting one or two parameters with the help of explicit formulas. Hence, band-pass filters of up to about 100 per cent fractional bandwidths can be designed, showing excellent symmetry without the need of numerical approximation procedures.