Least-squares monotonic lowpass filters with sharp cutoff

A new class of lowpass-filter functions with no finite zeros and a monotonic magnitude response is first derived by using a least-squares norm to minimise the passband attenuation, and these filter functions are then augmented by adding one pair or multiple pairs of j¿-axis zeros. The magnitude characteristics of these filters are compared with those of the generalised inverse Cheby¿shev filters and are found to be superior, both in the passband and in the stopband.