Details

The spectral density function for a stationary time series , with autocovariance function , can also be written as

The sdf can be interpreted as the amount of variability accounted for by a sinusoid with frequency .

Let . Then we can write where is an integer and . Then we see that . Consequently all such frequencies are said to be aliased with . The highest frequency that can be represented in a discrete time series sampled at times is 0.5 and is known as the Nyquist frequency. More generally, if the time interval between observations is then the Nyquist frequency is .