Frequency domain signal, origin

Processing in general transforms an original time domain signal s(t) with the aid of some processing function(s) into a manipulated frequency domain signal S"(f). Manipulations can be performed either in the time domain ( s(t) => s (t) ) prior to the Fourier transformation, or in the frequency domain (S (f) S"(f)) after the Fourier... 

Apart from some special drift processes that we will treat separately, the noise in the measurements is expected to be the result of random processes much faster than the changes in the useful signal itself. Fourier transform spectral methods exploit this difference in frequency for separating the two components by considering a frequency-domain representation of the signal instead of its original time domain representation. 

Historically, the first techniques designed to achieve independet control over pitch or duration were carried out in the time domain Fairbanks, Everitt and Jaeger s modified tape recorder [Fairbanks et al., 1954] probably is the first known automatic time-domain system for speech transposition. By contrast with frequency-domain methods, time-domain techniques for time or pitch scale modification manipulate short-duration time-segments extracted from the original signal, a mechanism usually called sampling or splicing As a result, they tend to require much fewer calculations and lend themselves quite well to real-time implementations. 

XQ(t) is found by twice integrating the acceleration (t) - Xo(t). This calculation is easily performed by a spectrum " analyzer since integration in the frequency domain is equivalent to dividing the Fourier transform of the original signal by j w. Thus... 

For the chemometric analysis of NMR spectral data it is generally assumed that the observed NMR data matrix is composed of spectra, (w), where each different yth spectrum covers a frequency range observable window (spectral window). It is also possible to perform chemometric analysis on the complex time domain signal, (t), which is the original form of the NMR data following quadrature detection. The time-domain signal and the frequency spectrum are related through a Fourier transformation... 

Fourier transform infrared spectroscopy (FTIR) had its origins in the interferometer developed by Michelson in 1880 and experiments by astrophysicists some seventy years later. A commercial FTIR instrument required development of the laser (1960, by Theodore H. Maiman [1927- ], Hughes Aircraft), refined optics, and computer hardware and software. The Fourier transform takes data collected in time domain and converts them to frequency domain, the normal infrared (IR) spectrum. FTIR provided vasdy improved signal-to-noise ratios allowing routine analyses of microgram samples. 

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