Generation of 1D and 2D analog and digital lowpass filters with monotonic amplitude-frequency response

In this work, we discuss a new design methodology to generate monotonic frequency-response filters. We start from Butterworth, Papoulis, Filanovsky and Bessel-Thomson filters. For each of these filters, all-possible lower-order filters having monotonic responses are segregated from the corresponding higher-order filters. These provide new sets of such filters. In addition, it is shown that higher order filters having monotonic responses can be obtained by appropriate combinations of the filters from these new sets. This permits one to generate a large number of low-pass 1D analog filters having monotonic responses. 2D filters having monotonic frequency responses are designed for the first time starting from the above proposed filters. The analog filters are obtained by suitably cascading the filters in s₁ and s₂ domains. Suitable 2D digital filters are obtained by employing the generalized bilinear transformations, the constants chosen to ensure stability and monotonicity. Suitable examples are provided