Using the quantum interference of photon pairs in N-stage nonlinear interferometers (NLIs), the contour of the joint spectral function can be modified into an islands pattern. We perform two series of experiments. One is that all of the nonlinear fibers in pulse pumped NLIs are identical; the other is that the lengths of N pieces of nonlinear fibers are different. We not only demonstrate how the pattern of spectral function changes with the stage number N, but also characterize how the relative intensity of island peaks varies with N. The results well agree with theoretical predictions, revealing that the NLI with lengths of N pieces of nonlinear fibers following binomial distribution can provide a better active filtering function. Our investigation shows that the active filtering effect of multi-stage NLI is a useful tool for efficiently engineering the factorable two-photon state—a desirable resource for quantum information processing.