The Fourier transform.

DNA's double helix, the sunspot cycle and the sawtooth signals of electronics can be reduced mathematically to a series of undulating curves. This idea underlies a powerful analytical tool T o calcu1ate a transform, just listen. The ear automatically performs the calcu1ation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting sound-the waves of pressure travel-ing through time and the atmosphere into a spectrum, a description of the sound as a series of volumes at distinct pitches. The brain turns this information into perceived sound Similar operations can be done by mathematical methods on sound waves or virtually any other fluctuating phenomenon, from light waves to ocean tides to solar cycles. These mathematical tools can decompose functions representing such fluctuations into a set of sinusoidal components undulating curves that vary from a maximum to a minimum and back, much like the heights of ocean waves. The Fourier transform is a function that describes the amplitude and phase of each sinusoid, which corresponds to a specific frequency. (Amplitude describes the height of the sinusoid; phase specifies the starting point in the sinusoid's cycle.) The Fourier transform has become a powerful tool in diverse fields of science. In some cases, the Fourier transform can provide a means of solving unwieldy equations that describe dynamic responses to electriCity, heat or light. In other cases, it can identify the regular contributions to a fluctuating RONAlD N. BRACEWEI.l. has been on the faculty of the electrical engineering department at Stanford University since 1955. He was educated at the University of Sydney and the Cavendish laboratory In Cambridge, England, where he got his Ph.D. His research interests have ranged over microwave radar, Ion-ospheric physics and radio astronomy_ At Stanford he is a member of the Space, Telecommunications and Radiosdence Laboratory and Is professor of computer SCience, by courtesy. signal, thereby helping to make sense of observations in astronomy, medicine and chemistry. T he world first learned about the technique from the mathematician for whom the transform is named, Baron Jean-Baptiste-Joseph Fourier. Fourier was not merely interested in heat; he was obsessed by it. He kept his home in Grenoble so uncomfortably hot that visitors often complained. At the same time he would cloak himself in heavy coats. Perhaps it was the lure of a warm climate that in 1798 drew Fol.\rier to join the retinue of 165 …