what kind of filter has the following property?

what kind of filter has the following property?

suppose the input signal f(x) = a0+a1*x+a2*x^2+a3*x^3+..., after
filtering, g(x)=h(x)*f(x). g(x) = a0+a2*x^2+a4*x^4+..., i.e. the filter
removes the odd polynomial components of the input signal f(x).