The effect of a certain sampling pattern in the frequency analysis is particularly transparent for the power spectrum. Let s be the sampling function taking on the value 1 at the (unevenly spaced) times of the observations observation and 0 elsewhere. The power spectrum of the sampling function
is an ordinary, non-random function called the spectral window
function. The discrete observations are the product of s and the
model function f: x = s f so that their transform is a convolution
of transforms: 
, where
and 
. For
and 
we obtain the result 
. Because of the linearity of
our result extends to any combination of frequencies.
Taking the square modulus of the result equation, we obtain both
squared and mixed terms. The mixed terms
correspond to an interference of
frequencies 
and 
differing by either sign or
absolute value. Therefore, if interference between frequencies is
small, the power spectrum reduces to the sum of the window functions
shifted in frequency:
In the opposite case of strong interference, ghost patterns may arise in the power spectrum due to interference of window function patterns belonging to positive as well as negative frequencies. The ghost patterns produced at frequencies nearby or far from the true frequency are called aliases and power leaks, respectively.