Generation of transfer functions yielding monotonic frequency responses by the integration of Butterworth polynomials

Starting from two lower order Butterworth polynomials, 1-D transfer functions are obtained by suitably integrating them and associating the same to the denominator of a transfer function. These functions guarantee monotonic response in the frequency domain. By suitable association of the polynomials obtained by integration, higher order functions yielding monotonic responses are obtained. These can be readily used to obtain 1-D and 2-D discrete filters yielding such responses.