Signal processing Fourier transform techniques

Before 1989, Fourier transform (FT) and fast Fourier transform (FFT) were employed mainly by chemists to manipulate data from analytical studies [5-7]. After the publication of an important paper by Daubechies [8] in 1988, a new transformation algorithm called wavelet transform (WT) became a popular method in various fields of science and engineering for signal processing. This new technique has been demonstrated to be fast in computation, with localization and quick decay properties, in contrast to existing methods such as FFT. A few chemists have applied this new method for... 

Each signal sequence A or B will be processed separately by using the Fourier transform and CFAR target detection techniques. A single target with specific range and velocity will be detected in both sequences... 

On the other hand, additional spectroscopic information can be obtained by making use of this technique The Fourier transform of the frequency-filtered transient (inset in Fig. 8) shows that the time-dependent modulations occur with the vibrational frequencies of the A E and the 2 IIg state. In the averaged Na2+ transient there was only a vanishingly small contribution from the 2 IIg state, because in the absence of interference at the inner turning point ionization out of the 2 IIg state is independent of intemuclear distance, and this wavepacket motion was more difficult to detect. In addition, by filtering the Na2+ signal obtained for a slowly varying pump-probe delay with different multiples of the laser frequency, excitation processes of different order may be resolved. This application is, however, outside the scope of this contribution and will be published elsewhere. 

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.). 

Whereas electroreflectance is conventionally used in the UV/visible region, in the 1980s Bewick et al.l2 14 developed the technique in the IR region. Since IR radiation interacts with the vibrations of chemical bonds, important information regarding bonds with adsorbed species has been obtained15, especially useful for research into electrocatalysts. New developments in signal processing, such as the Fourier transform (FT-IR), have veen very valuable. 

There are numerous books on digital signal processing (DSP) and Fourier transforms. Unfortunately, many of the chemically based books are fairly technical in nature and oriented towards specific techniques such as NMR however, books written primarily by and for engineers and statisticians are often quite understandable. A recommended reference to DSP contains many of the main principles [29], but there are several similar books available. For nonlinear deconvolution, Jansson s book is well known [30]. Methods for time series analysis are described in more depth in an outstanding and much reprinted book written by Chatfield [31]. 

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