The signal detection problems facing those who search the sky for evidence of extraterrestrial civilizations or interesting natural phenomena are enormous. Among those problems are the fact that we don't know much about what to expect. In particular, we don't know exactly where to look in the sky, or what frequencies might be used, or the possible forms of the transmissions. Moreover, the many powerful sources of natural and terrestrial sources of interfering signals must not be confused for extraterrestrial ones. There is also the massive computer power required, which has driven the development of specialized hardware and software as well as distributed computation over thousands of Internet-connected personal computers across the world using the SETI@home computational screen-saver. Although many of the computational techniques used in this search are far more sophisticated than those covered in this web site, they begin with the basic concepts covered here.
One of the reoccurring themes of this site has
been that the more you know about your data, the more
likely you are to obtain a reliable measurement. In the
case of possible extraterrestrial signals, we don't know
much, but we do know a few things.
We know that electromagnetic radiation over a wide range of frequencies is used for long-distance transmission on earth and between earth and satellites and probes far from earth. Astronomers already use radio telescopes to receive natural radiations from vast distances. In order to look at different frequencies at once, Fourier transforms of the raw telescope signals can be computed over multiple time segments. We previously saw a simulation that showed how hard it is to see a periodic component in the presence of on equal amount of random noise and yet how easy it is to pick it out in the frequency spectrum.
Also, transmissions from extraterrestrial civilizations might be in the form of equally-spaced pulses, so their detection and verification is also part of SETI signal processing. Interestingly, triplets and other groups of equally spaced pulses appear in the Fourier transforms of high frequency carrier waves that are amplitude or frequency modulated (like AM or FM radio). Of course, there is no reason to assume, nor to reject, that extraterrestrial civilizations might use the same methods of communication as ourselves.
One thing that we know for sure is that the earth rotates around its axis once a day and that it revolves around the sun once a year. So if we look at a fixed direction out from the earth, the distant stars will seem to move in a predictable pattern, whereas terrestrial sources will remain fixed on earth. The huge Arecibo Observatory dish in Puerto Rico is fixed in position and is often used to look in one selected direction for extended periods of time. The field of view of this telescope is such that a point source at a distance takes 12 seconds to pass. As SETI says: "Radio signals from a distant transmitter should get stronger and then weaker as the telescope's focal point moves across that area of the sky. Specifically, the power should increase and then decrease with a bell shaped curve (a Gaussian curve). Gaussian curve-fitting is an excellent test to determine if a radio wave was generated 'out there' rather than a simple source of interference somewhere here on Earth, since signals originating from Earth will typically show constant power patterns rather than curves". Also, any observed 12 second peaks can be re-examined with another focal point shifted towards the west to see if it repeats with the expected time and duration.
We also know that there will be a Doppler shift in the frequencies observed if the source is moving relative to the receiver; this is observed with sound waves as well as with electromagnetic waves like radio or light. Because the earth is rotating and revolving at a known and constant speed, we can accurately predict and compensate for the Doppler shift caused by earth's motion (this is called "de-chirping" the data).
For more on the details of SETI signal processing, see SETI@home.