# Frequency Noise

Definition: noise of the instantaneous frequency of an oscillating signal

German: Frequenzrauschen

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

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 Hz^{2}/Hz) is directly related to that of the phase noise:

where *f* is the noise frequency.
For example, white frequency noise (*S*_{ν}(*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.

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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