The signal processing-system using singularity is provided which is excellent in determination of the original signal against the degradation environment of an operating condition and robust to the signal degradation of noise, can generate the signal suitable to regeneration of the original signal, and has regeneration means to regenerate the original signal, wherein the system comprises: an original signal converter of the signal processing-system which converts the original signal contained in the inputted signal into the signal containing singular points by using the specific function, the converter outputting the signal containing singular points; an original signal regenerator which converts the incoming signals containing singular points into signals having singular points by the specific signal processing, the regenerator extracting the undesired-signal component from the signals having singular points; and a regenerator which regenerates the original signal by carrying out the operation of the generated undesired-signal and the above-mentioned signal-containing-singular-points, and outputs the regenerated signal.