Stability Measures for Frequency Sources - Understanding GPS: Principles and Applications - page 666

A common method used to measure oscillator stability is based on the instanta-
neous fractional frequency deviation from the nominal frequency

0 given by

φ
πν

()

yt =

2

0

The power-law spectral densities of the five random frequency noise processes
mentioned in Section B.1 can be represented in the frequency domain by the sum of
five independent noise processes as [1]:

+
∑

2

()

α

Sf = hf for 0 < f f <

y α h

α =− 2

= 0 for ff ≥

h

where:

h α = constant

α = integer

f h = high-frequency cutoff of an infinitely sharp lowpass filter

This power spectral density is visually represented in Figure B.1 for the five ran-
dom frequency noise processes: random walk frequency, flicker frequency, white
frequency, flicker phase, and white phase.

White phase

f − 2

Random walk frequency

f 2

Flicker phase

Flicker frequency

f 1

f − 1

White frequency

f 0

Log frequency, f

Figure B.1 Power spectral densities for five random frequency noise processes: random walk fre-
quency, flicker frequency, white frequency, flicker phase, and white phase.