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Frequency Noise

Definition: noise of the instantaneous frequency of an oscillating signal

German: Frequenzrauschen

Category: fluctuations and noise

How to cite the article; suggest additional literature

Author:

The term frequency noise refers to random fluctuations of the instantaneous frequency of an oscillating signal. The instantaneous frequency is defined as

instantaneous frequency

i.e. essentially as the temporal derivative of the oscillation phase φ. Any random deviation from a purely linear phase evolution is seen as frequency noise.

The power spectral density of frequency noise (with units of Hz2/Hz) is directly related to that of the phase noise:

power spectral density of frequency noise

where f is the noise frequency. For example, white frequency noise (Sν(f) = const) corresponds to phase noise with a power spectral density proportional to f−2. In that case, the linewidth is π times the one-sided power spectral density of the frequency noise (or 2π times the two-sided power spectral density). Such a situation occurs e.g. in a single-frequency laser which is only subject to quantum noise and exhibits the Schawlow–Townes linewidth.

Phase noise or frequency noise are just different ways of describing the same phenomenon. However, numerical processing of frequency noise rather than phase noise can have technical advantages in certain situations.

Questions and Comments from Users

2020-09-20

I think there is an error in this sentence: “The power spectral density of frequency noise (with units of Hz2/Hz)...”

The unit should probably be rad2/Hz?

Answer from the author:

No, the instantaneous frequency has units of Hertz, not radians. However, you often find units of rad2/Hz in the literature; these refer to Sφ(f), the noise PSD of the optical phase, which is directly related to frequency noise as explained in the article.

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See also: phase noise, power spectral density, linewidth, laser noise, coherence, coherence time
and other articles in the category fluctuations and noise

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