This paper addresses the noise estimation in the digital domain and proposes a noise estimator based on the step signal model. It is efficient for any distribution of noise because it does not rely only on the smallest amplitudes in the signal or image. The proposed approach uses polarized/directional derivatives and a nonlinear combination of these derivatives to estimate the noise distribution (e.g., Gaussian, Poisson, speckle, etc.). The moments of this measured distribution can be computed and are also calculated theoretically on the basis of noise distribution models. The 1D performances are detailed, and as this paper is mostly dedicated to image processing, a 2D extension is proposed. The 2D performances for several noise distributions and noise models are presented and are compared with selected other methods.