Needless to say, it's quite unlikely that an alien planet will be at rest with respect to Earth. You may remember that we (and our telescope in Arecibo) are whizzing along on a rotating planet which is revolving around the Sun, which in turn is orbiting the center of our Milky Way galaxy, etc. We can assume that our extra-terrestrial friends are likewise situated.
Radio waves emitted from a moving source and/or received by a moving target show a phenomenon called "the Doppler effect."
For example, when you hear a car honking as it passes you, the frequencyor pitchof the sound changes as the car passes.
Although our remote friends aren't honking their horns at us, they are sending waves (electromagnetic waves) at us. Their signal will be distorted by the mutual motions of our two systems in much the same way that moving car horns are distorted. This "chirped" signal would appear to change in frequency over time, as shown by the figure to the right. To control for chirping, the SETI@home screensaver analyzes the data many times over trying a great variety of possible Doppler accelerations. First, the screensaver mathematically "undoes" a specific doppler acceleration or "chirp" from the data. It then feeds the resulting "de-accelerated" data to the FFT (Fast Fourier Transform) routines. This is called "de-chirping" the data. SETI@home performs this procedure at many points between -50 Hz/sec to +50 Hz/sec. At the finest frequency resolution of 0.075 Hz, we check for 5409 different chirp rates between -10 Hz/sec and +10 Hz/sec!