Monotonic step response filters with maximum asymptotic cutoff

Transfer functions are derived which yield a monotonic step response, or equivalently positive impulse response, and which yield maximum asymptotic cutoff for the degree of the network. The impulse response of the networks is approximated accurately by
h_{n}(t)=K_{n}(sin{\pi}t)^{n}, 0
<
t
<
1
_{n}(t)=0, 1 < t
The transfer functions are all ladder realizable requiring no redundant elements.