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Signal detection theory: Signals and noise

If you read a paper by a communications engineer, a cognitive psychologist, or an artificial intelligence researcher, chances are that you'll run into signal detection theory. Here's a quick primer on the subject.

We begin with the idea that we are trying to measure a signal, maybe a message sent by another person. We can call ourselves (together with our equipment) a receiver, and we can call the originator of the signal (together with their equipment) an emitter. Perhaps they are sending Morse code signals from a ship at sea using a light source, and we are receiving miles away using a digital video camera containing photo sensors. The simplest case is one in which the signal can be in one of two states: present or absent, \on" or "off."

A problem arises for us as the receiver, because we can almost never eliminate unwanted sources of activity in our equipment that disturb measurements of the signal of interest. Collectively, these nuisance sources of activity are called noise. Noise may arise from additive contamination by ambient sources of the same kind of received energy (in this case, light), or it may arise from the properties of our measurement equipment, such as thermal noise.

If we take many measurements of an "on" signal plus noise, and many measurements of the noise alone, we will see that many of the same measurements show up under both conditions (see figure below). We can make histograms of our measurements, counting the number of times each value is measured, and these can be fit with smooth probability density functions. Just looking at our instruments, it can sometimes be difficult to judge whether the signal was "present" or "absent." A standard approach is to find a cutoff value on measurements, or a criterion for judgment, that makes the best possible guess.

We will explore how this is done in part 2 of this posting. 

For other background information check out our post on signals, sensors and data

The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author.

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