Detection

Abstract

Detectors are tools which extract and emphasize important features of a signal. In order to be useful, a detector should be functorial, in that it preserves the features of the signal. In most practical settings, it is desirable for detectors to be lossy. Specifically, one usually wants to transform a signal into a representation that removes noise and irrelevant signals. Merely requiring that certain qualitative features of a signal be preserved will motivate our definition of detectors as certain kinds of forgetful functors. These ideas are showcased in a crucial way in two contexts; that of sampling theory and mapping a radio network.