4-27
    In the frequency domain, due to the phase deviation, f(t), some of the power is at frequencies other than n0.  The stabilities are characterized by "spectral densities."  The spectral density, SV(f), the mean-square voltage <V2(t)> in a unit bandwidth centered at f, is not a good measure of frequency stability because both e(t) and f(t) contribute to it, and because it is not uniquely related to frequency fluctuations (although e(t) is often negligible in precision frequency sources.)      The spectral densities of phase and fractional-frequency fluctuations, Sf(f) and Sy(f), respectively, are used to measure the stabilities in the frequency domain.  The spectral density Sg(f) of a quantity g(t) is the mean square value of g(t) in a unit bandwidth centered at f.  Moreover, the RMS value of g2 in bandwidth BW is given by
Spectral Densities
   The Fourier frequency is a fictitious frequency used in Fourier analysis of a signal.  Zero Fourier frequency corresponds to the carrier, and a negative Fourier frequency refers to the region below the carrier.  The integral of the spectral density over all Fourier frequencies from minus infinity to infinity is the mean-square value of the quantity.  The spectral density of phase-noise Sf(f') is important because it is directly related to the performance of oscillators in RF signal processing applications.  Up until 1988, the single-sideband (SSB) noise power per Hz to total signal power ratio was often specified for oscillators instead of the phase spectral density.  This ratio has been designated L(f).  In IEEE standard 1139-1988 (current version is 1139-1999), the definition of L(f) was changed to one-half Sf(f').  When defined this way, L(f) is equal to the SSB noise-to-signal ratio only as long as the integrated phase-noise from f' to infinity is small compared to one rad2.
   The phase spectral density (phase noise) depends on carrier frequency.  When the signal from an oscillator is multiplied by n in a noiseless multiplier, the frequency modulation (FM) sidebands increase in power by n2, as does the spectral density of phase.  Consequently, it is important to state the oscillator frequency together with the phase noise.