A filter is a linear operation that converts one time series into another (Chatfield, 1995). Low-pass, band-pass and high-pass filters are used to separate different signals from a time series.
Application of a low pass filter to a climate time series removes high frequency fluctuations from the time series. Figure 1 shows a time series of daily maximum temperature 30 year (1971 - 2000) averages, containing high frequency signal, and a smooth fit to this using Equation 1. This smooth fit is an example of a low pass filter.
Chatfield, C, 1995, The analysis of Time Series, 4th edition. Chapman & Hall