The purpose of this invention is that the optimum approximation formula can be derived even if an analysis filter has non-linear characteristic in a discrete signal approximation system. The norm of source signal 1 is bounded. Analysis filters 2 of FIR filters yield the output signal that is expressed with polynomial of transformed source signal 1 through a unit filter. An interpolation function is calculated according to the filter characteristic based upon the multi-dimensional function transformed from the polynomial. The output signal of the analysis filter 2 is sampled after each constant interval to obtain a discrete signal. The approximation function of the power function of the source signal 1 is calculated with linear combination of the interpolation functions using the discrete signals as coefficients. The radical of this approximation function is calculated to derive the root approximation function of the source signal 1. The root approximation functions of all sampling timings are composed to make a total approximation function.