The Photonics Spotlight
Signal-to-Noise Ratio and Measurement Bandwidth
Posted on 2009-07-21 as a part of the Photonics Spotlight (available as e-mail newsletter!)
Permanent link: https://www.rp-photonics.com/spotlight_2009_07_21.html
Abstract: It is explained why it is meaningless to specify some signal-to-noise level without the corresponding measurement bandwidth.
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 …
This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the Encyclopedia of Laser Physics and Technology.
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