Signal-to-Noise Ratio and Measurement Bandwidth

Posted on 2009-07-21 as a part of the Photonics Spotlight.

Permanent link: http://www.rp-photonics.com/spotlight_2009_07_21.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: encyclopedia articles on noise specifications, power spectral density

Even in scientific papers, I encounter fairly frequently the following situation. There is some kind of RF spectrum exhibiting a narrow-band signal and a noise background, and the authors report that the signal is higher than the noise by some number of decibels. However, a measurement bandwidth is not specified. The same happens in situations where there is an optical spectrum with some narrow-band laser line and an ASE background.

The trouble is that the number of these decibels (often interpreted as some signal-to-noise ratio) depends on the measurement bandwidth. If the spectrum displays some kind of power in a certain (possibly not specified) bandwidth, a narrow-band signal (i.e., a signal with a bandwidth well below the measurement bandwidth) will lead to a peak height which is not dependent on the measurement bandwidth. On the other hand, the measurement bandwidth will directly affect the noise level: the larger the measurement bandwidth, the more noise is captured. This means that such kind of signal-to-noise ratio is meaningless if the measurement bandwidth is not specified. Needless to say, meaningless statements shouldn't have a place in scientific papers …