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The Spectrum of Periodic Signals Signals dwell both in the time and frequency domains; we can equally accurately think of them as values changing in time (time domain), or as blendings of fundamental frequencies (spectral domain). The method for determining these fundamental frequencies from the time variations is called Fourier or spectral analysis. Similar techniques allow returning to the time domain representation from the frequency domain description. | Digital Signal Processing A Computer Science Perspective Jonathan Y. Stein Copyright 2000 John Wiley Sons Inc. Print ISBN 0-471-29546-9 Online ISBN 0-471-20059-X 3 The Spectrum of Periodic Signals Signals dwell both in the time and frequency domains we can equally accurately think of them as values changing in time time domain or as blendings of fundamental frequencies spectral domain . The method for determining these fundamental frequencies from the time variations is called Fourier or spectral analysis. Similar techniques allow returning to the time domain representation from the frequency domain description. It is hard to believe that 300 years ago the very idea of spectrum didn t even exist that less than 200 years ago the basic mechanism for its calculation was still controversial and that as recently as 1965 the algorithm that made its digital computation practical almost went unpublished due to lack of interest. Fourier analysis is used so widely today that even passing mention of its most important applications is a lengthy endeavor. Fourier analysis is used in quantum physics to uncover the structure of matter on the smallest of scales and in cosmology to study the universe as a whole. Spectroscopy and X-ray crystallography rely on Fourier analysis to analyze the chemical composition and physical structure from minute quantities of materials and spectral analysis of light from stars tells us of the composition and temperature of bodies separated from us by light years. Engineers routinely compute Fourier transforms in the analysis of mechanical vibrations in the acoustical design of concert halls and in the building of aircraft and bridges. In medicine Fourier techniques are called upon to reconstruct body organs from CAT scans and MRI to detect heart malfunctions and sleep disorders. Watson and Crick discovered the double-helix nature of DNA from data obtained using Fourier analysis. Fourier techniques can help us differentiate musical instruments made .