Summary: We present an approach to the analysis of signals based on analog representation of measurements. Methodologically, it relies on the consideration and full use of the continuous nature of a realistic, as opposed to an idealized, measuring process. Mathematically, it is based on the transformation of discrete or continuous signals into normalized continuous scalar fields with the mathematical properties of distribution functions. This approach allows a simple and efficient implementation of many traditionally digital analysis tools, including nonlinear filtering techniques based on order statistics. It also enables the introduction of a large variety of new characteristics of both one- and multi-dimensional signals, which have no digital counterparts.