Least Lp-norm low-pass filter

We know that least Lp-norm filters, processing a one-dimensional signal within a time window, are suitable for attenuation of impulses. This article proposes a new analogue filter with exponentially weighted old samples, which is a generalization of the first-order low-pass filter. The obtained formula describing the output signal is presented in an implicit form. A simple but always convergent algorithm facilitates the approximation of the signal. Conducted simulations show properties of a set of the analogue filters with different values of p in the range of 1 to 2, covering step, ramp, and sinusoidal responses, as well as the ability to attenuate random noises, including stable distributions. The results prove that the elaborated filters achieve steady states faster than the typical low-pass filter and are particularly useful in the suppression of impulses. This property makes it possible that such a filter is perfectly adequate as an input filter of measurement transducers.