Monotonic low-pass filters with improved stopband performance

A new class of monotonic low-pass filter functions which derives its origin from a method of determining optimum monotonic lowpass filters described by Halpern is introduced. These functions yield a very flat passband response and a considerably higher attenuation rate than the all-pole Butterworth functions. It is also shown by a numerical example that they compare favorably with the maximally flat rational approximants with one pair of imaginary-axis zeros when the comparison is made on the basis of equal complexity of the resulting network.