Shadow filters generalisation to nth-class

The theory of shadow filters, a new family of second-order filters recently introduced, is extended to class n filters, where n is a positive integer. It is shown that their centre frequency f_0An is given by f_0An=f₀(1-A)^n/2 where f₀ is the centre frequency of the starting unity gain filter and A the gain of amplifiers. Simulation results of a practical example implemented for n=2 are given. They entirely confirm the theoretical analysis.