Signal-to-noise Ratio

What is a Signal-to-noise Ratio?

A Signal-to-noise ratio is a measure of the amount of background noise with respect to the primary input signal. It is formally defined as he ratio of signal power to noise power, and is often expressed in decibels. For example, a ratio of 1:1 indicates more signal than noise, and is greater than 0 decibels (dB). The Signal-to-noise ratio (SNR) is often referenced regarding electrical signals, however it can be applied to any form of signal including audio, financial trading, or isotope levels in an ice core. Informally, the SNR is sometimes defined as the ratio of useful information to irrelevant information in conversation or data exchange.

How does the Signal-to-Noise Ratio work?

The SNR defines the ratio of the power of a signal to the present background noise. In order for the SNR to accurately describe the data, both the power of the signal and the background noise must be measure at the same or equivalent points in a system of reference. For example, the signal cannot be measured in dB when the noise is measured in watts. The written definition of the SNR is:

Source

Signal-to-noise vs. Dynamic Range

While the two concepts are similar, they differ in the ways in which the signal is measured. For example, when the ratio is measured between the strongest un-distorted signal and the minimum discernible noise level, it is defined as the dynamic range. The signal-to-noise ratio differs in that it measures an arbitrary signal level, not always the most powerful signal. In this sense, the SNR is conceptually thought of as the average signal-to-noise ratio.

An Example of Signal-to-Noise Ratio

Let's imagine two people are having a conversation when a loud truck appears. The truck's engine hums at a steady 50dB, making the conversation challenging to hear. If one of the people is speaking a whisper at 30dB, it will be hard for the other person to hear them. However, if the other person begins shouting at 80dB, their voice would be louder than the 50dB produced by the truck and the other person would be able to hear the conversation. If the person's shouting voice is considered the signal and the engine the noise, the signal-to-noise ratio would be 30dB.