A white noise process is called a strict-sense white noise process if the noise samples at distinct instants of time are independent. A white Gaussian noise process is a strict-sense white noise process. Such a process represents a ‘purely' random process, because its samples at arbitrarily close intervals also will be independent.
Example 1 A random-phase sinusoid corrupted by white noise
Suppose where is
a constant bias and and is a zero-mean WGN process with PSD of and independent of Find and
where 
is
a constant bias and
and 
is a zero-mean WGN process with PSD of 
and independent of 
Find 
and 
