Editing Additive white Gaussian noise (section)

==Effects in time domain==
[[File:Zero crossing.jpg|thumb|300px|Zero crossings of a noisy cosine]]

In serial data communications, the AWGN mathematical model is used to model the timing error caused by random [[jitter]] (RJ).

The graph to the right shows an example of timing errors associated with AWGN. The variable Δ''t'' represents the uncertainty in the zero crossing. As the amplitude of the AWGN is increased, the [[signal-to-noise ratio]] decreases. This results in increased uncertainty Δ''t''.<ref name="rrd"/>

When affected by AWGN, the average number of either positive-going or negative-going zero crossings per second at the output of a narrow bandpass filter when the input is a sine wave is

: <math>
\begin{align}
& \frac{\text{positive zero crossings}}{\text{second}} = \frac{\text{negative zero crossings}}{\text{second}} \\[8pt]
= {} & f_0 \sqrt{\frac{\text{SNR} + 1 + \frac{B^2}{12f_0^2}}{\text{SNR} + 1}},
\end{align}
</math>

where
: ''ƒ''<sub>0</sub> = the center frequency of the filter,
: ''B'' = the filter bandwidth,
: SNR = the signal-to-noise power ratio in linear terms.