On nonlinear filters involving transformation of the time variable

A new type of nonlinear filter, called the -filter, is introduced that involves a transformation of the independent variable of the input function. It is shown how an -filter can be designed to filter out superimposed "noise" on a signal, leaving the large peaks of the signal unattenuated. Unlike a Iow-pass linear filter, the low-pass -filter is almost frequency independent and so does not affect the amplitudes of large sharp peaks of the signal. It is shown that the -filter can be realized in real time and that a wide class of -filters have a filtering action which is independent of the dc level of the input signal.