Gibbs phenomenon on sampling series based on Shannon's and Meyer's wavelet analysis

We deal with the maximum Gibbs ripple of the sampling wavelet series of a discontinuous function f at a point t ∈R, for all possible values of a satisfyingf(t)=αf(t−0)+(1−a)f(t+0). For the Shannon wavelet series, we make a complete description of all ripples, for any a in [0,1]. We show that Meyer sampling series exhibit Gibbs Phenomenon for α<0.12495 and α>0.306853. We also give Meyer sampling formulas with maximum overshoots shorter than Shannon's for several α in [0,1].