Fourier transform data-processing techniques

Gillette PC, Lando JB, Koening JL (1985) A survey of infrared spectral data processing techniques In Ferraro JR, Basile LJ (eds) Fourier transform infrared spectroscopy -applications to chemical systems, Vol 4 Academic Press, New York, 1-47 Graham JA, Grim WM III, Fateley WG (1985) Fourier transform infrared photoacoustic spectroscopy of condensed-phase samples, In Ferraro JR, Basile LJ (eds) Fourier transform infrared) spectroscopy - applications to chemical systems, Vol 4 Academic Press, New York, 345-392... 

The frequency-domain format eliminates the manual effort required to isolate the components that make up a time trace. Frequency-domain techniques convert time-domain data into discrete frequency components using a mathematical process called Fast Fourier Transform (FFT). Simply stated, FFT mathematically converts a time-based trace into a series of discrete frequency components (see Figure 43.19). In a frequency-domain plot, the X-axis is frequency and the Y-axis is the amplitude of displacement, velocity, or acceleration. 

Particle shapes influence properties such as surface area, bulk density, flow, and so on. A number of methods are available for describing shape from simpler qualitative descriptions, through property ratios, to techniques that employ fast Fourier transformations to describe the projected perimeter of the particle. The measurement of the shape and the relevance of the data obtained are generally the two difficulties associated with particle shape. Fortunately, in the processing of materials physically unlike those in chemical processing, shape is perhaps is less significant and is more often than not inherently accounted for in the nominal diameter. 

Radiofrequency spectroscopy (NMR) was introduced in 1946 [158,159]. The development of the NMR method over the last 30 years has been characterised by evolution in magnet design and cryotechnology, the introduction of computer-based operating systems and pulsed Fourier transform methods, which permit the performance of new types of experiment that control production, acquisition and processing of the experimental data. New pulse sequences, double-resonance techniques and gradient spectroscopy allow different experiments and have opened up the area of multidimensional NMR and NMRI. 

One of the principal contributions of electronic data processing over the past several years in terms of chemical analysis is the saving of manual effort in interpreting analytical data. Special techniques, such as Fourier transform, have increased speed (as well as sensitivity) by orders of magnitude in connection with infrared, nuclear magnetic resonance, and mass spectroscopy, Of course, for on-line process analyses, essentially instantaneous interpretation is required to provide the proper error signal that is used to position the final control element (valve, feeder, damper, etc.). 

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