Researchers at the Technion-Israel Institute of Technology have discovered a means of identifying and neutralizing the frequency of pirate radio stations within seconds. Radio signals from such illegal radio stations - which pose a security danger to airports and defense - currently take many hours to locate. The "breakthrough" discovery, announced Monday, has aroused much interest around the scientific world, and the Technion has registered a patent for it and set up a company for its development. Technion doctoral student Moshe Mishali of the electrical engineering faculty, who made the discovery together with his supervisor Prof. Yonina Eldar, said there are other important applications of the discovery - including expanding the memory of sound recorders and significantly improving magnetic resonance imaging scanners for medical uses, as well as for various defense purposes. They noted that there are "kits" on Web sites to build a pirate radio station within less than an hour. But with the Technion discovery, the frequency at which the station is broadcasting illegally can be identified within seconds and eliminated. The two Technion scientists worked on numerous complicated algorithms and managed to "break" the fundamental barrier of the Nyquist-Shannon sampling theorem, which was formulated in 1928 by Harry Nyquist and proven by Claude Shannon in 1949. The theorem deals with the hypothetical spectrum of a band-limited signal as a function of frequency. It is a foundational result in the field of information theory, particularly in telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence. The theorem postulated that an analog signal that has been digitized can be perfectly reconstructed and leads to a formula for reconstruction of the original signal. "Digital devices take the physical signal and store it in a computer in a series of bits," explained Eldar. "The ear can't hear numbers, of course. Here the process of sampling and reconstruction comes in. In the sampling stage, we move from the physical signal to a series of numbers. The digital tape samples the signal that is heard and translates it into a series of bits - that is, zeroes and single digits. The process of reconstruction is the opposite - in which bits turn into physical signals that we hear or see in applications of a digital photo." The Nyquist-Shannon theorem has been studied for many years as a fundamental basis for sampling. Mishali and Eldar aimed at programming a sampling system for signals with many broadcasting tracks so the system could sample and reconstruct these signals at a significantly slower pace than what exists today. The breakthrough, they said, was accomplished by taking advantage of the fact that in parts of the spectrum, there is no broadcast. They cannily took advantage of the "holes" in the spectrum to slow down the sampling pace without harming the signal, Eldar explained.