Title: Filters high pass

High pass filters retain only high frequency signals in a time series. Figure 1 illustrates the separation of the high frequency variability of the temperature over one year by removing (subtracting) the fit to the annual cycle using the low pass filter developed in previous section.

Time series of daily temperature for one year with 30 year fitted sin/cos function (top) and the difference n=between these two (bottom)
Figure 1. Difference between original time series and a low pass filter (top) results in a time series containing only high frequencies (bottom) in Tmax series at Bismarck, North Dakota

High pass filters allow the analysis of variability on shorter time scales.