Deconvolution,

The deconvolution technique generally involves several steps  

The deconvolution procedure is typically repeated iteratively in order to obtain the best results. At iteration, the lineshape is adjusted in an attempt to provide narrower bands without excessive distortidhv There are three parameters that can be adjusted to tune, the 

With Deconvolution 1 you have access to a fully automatic and interactive mode. In the automatic mode only the region used for deconvolution and a few optional parameters (type of lineshape. number of peaks,. ..) may be set. Whilst the interactive mode allows you to set the initial values for the parameters controlling the iterative fitting process and to create, edit and delete peaks. 

Use the same spectrum and explore the options available with the highly 

There is an alternative to curve-fitting when it comes to the analysis of highly overlapped bands, and that is spectral deconvolution. Deconvolution describes the process of artificially increasing the apparent resolution of the spectrum so that the FWHM of peaks is significantly reduced. 

The most common form of deconvolution is Fourier self-deconvolution, which, as the name implies, takes place in the Fourier (time) domain. Deconvolution in the frequency domain is extremely arduous and lengthy. In the time domain, however, deconvolution equates to multiplication—and is therefore much quicker, even after taking into account the extra processing required for the FFT and IFFT. The procedure requires a knowledge of the band shape and full width, half-maximum resolution of the peaks involved. It is also common to enter a resolution enhancement factor—i.e. how much we want to improve the resolution by. As deconvolution is tremendously sensitive to noise, do not attempt it if the signal-to-noise ratio is less than a hundred. Also, enhancement factors tend not to be much greater than 2.5, owing to the noise amplification that occurs. 

Other methods are available for deconvolution. One of the most successful of these is maximum likelihood deconvolution. Although a description of this subject is outside the scope of this text, maximum likelihood can give results that are generally superior to Fourier selfdeconvolution. The maximum likelihood algorithm works by searching a response surface of all selected variables until it finds the most likely deconvolution based on the information content of the data. 

Maximum entropy is similar in some respects to maximum likelihood, although the technique is perhaps a little more esoteric and requires more expensive hardware and software. Nevertheless, the proponents of maximum entropy argue that it is the best possible solution to a problem such as deconvolution, as probability calculus is employed in the calculation of the most likely (maximum entropy) solution. 

All the methods outlined, with the exception of peak-picking and baseline correction, will lead to a reduction in the signal-to-noise quality of the specrum. This should be considered before the raw data are recorded, as signal-to-noise cannot be increased after the event. Bear in 

The overlaid peaks of the simulation were separated with the vertical separation method for area integration. For comparison, the overlaid peaks of the simulation were separated with the recommended curve fitting by Mr Westerberg (deconvolution) using the Gauss curve model. 

The values, from the report of A.W. Westerberg received and used as the target of the simulation area, were compared with the results of Vertical skim and the deconvolution. This comparison is shown in Table 7.1. 

The thick black peaks in Table 7.1 are those within the simulation that are overlapping in great areas. 

So peaks 6 and 10 are shoulder peaks with a very low resolution. 

P ak Ar a as it should bo Peak area Deviation from the area as it should be (%) Peak area Deviation from the area as it should be (%) 

This application is based on the method described by Griffiths and Pariente [446,447]. Two filters are employed. An exponential filter is used to sharpen spectral features the constant y is varied to change the filter shape. The y parameter 

As FSD tends to increase the apparent noise in the data, there is some benefit to be gained by simnltaneonsly applying a low-pass smoothing filter. This can effectively rednce the noise, which may be at a higher spatial frequency than the peaks, withont losing peak resolntion. The forms of the filters are boxcar and Bessel, and are mathematically described in the following. 

The deconvolntion filter is a simple exponential filter of the form e where y is the deconvolntion filter constant and X is the array (i.e., data file) whose X-axis range is normalized between 0 and 1. This function is multiplied by the Fourier transformed trace, and the data is then reverse Fourier transformed to give the result. 

The noise filter procedure consists of selecting the appropriate filter parameters, which is critical in obtaining good (and valid) results with FSD. 

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In fact a sensor measures a flow and proceeds an integration of across a surface, which operates as a spacial lowpass filter. To avoid a critical deconvolution, the error due to this integration must be kept negligible. 

To improve URT, we used a deconvolution technique. Our enhancement procedure is based on Papoulis deconvolution i.e. on an extension of the generalized inversion in the complementary bandwidth of the electro-acoustic set-up. 

Low and High frequency can be restored by use of a deconvolution algorithm that enhances the resolution. We operate an improvement of the spectral bandwidth by Papoulis deconvolution based essentially on a non-linear adaptive extrapolation of the Fourier domain. 

The deconvolution is the numerical solution of this convolution integral. The theory of the inverse problem that we exposed in the previous paragraph shows an idealistic character because it doesn t integrate the frequency restrictions introduced by the electro-acoustic set-up and the mechanical system. To attenuate the effect of filtering, we must deconvolve the emitted signal and received signal. 

In the remainder of this paper, we exhibit the solution of the deconvolution problem in the frequency domain, but it is possible to establish an analogy with tlie temporal solution exposed by G. Demoment [5,6]. 

We, now, illustrate result given by Papoulis deconvolution, reduced to its first iterate. 

Figure n°2 First Order Papoulis Deconvolution by the response of the system ha (response to a copper wire) (a) Time-sinogram (b) Image... 

To restore resolution, we proposed a signal processing method based on Papoulis deconvolution. We implemented this algorithm and tried to operate an improvement from an aluminum rod smaller than the wavelength. 

Lasaygues, P.,. Lefebvre, J.P., and Mensah S., Deconvolution and Wavelet Analysis on Ultrasonic Reflection Tomography, III International Workshop, Advances in Signal Processing for Non Destructive Evaluation of Materials, Quebec, Canada, (1997). 

The evaluation of the deconvolution results show that time resolution is better or equal to 1 with the chosen processing time unit of 0.08 microseconds (respectively a rate of 12.5 MHz). First signals processed conservatively have been acquired with a samplerate of 12.5 MHz. A Fourier analysis shows that the signals spectras do not have energy above 2.0 MHz. This means that a sampling rate of 4.0 MHz would have done the job as well. Due to the time base of the ADC an experimental check with a sample rate of 5.25 MHz has been carried out successfully. 

Gut, R, Kreier, P., Moschytz, G.S. Trellis Based Deconvolution of Ultrasonic Echoes Proc. of IEEE International Symposium on Circuits and Systems, Vol. 2, Seattle, May 1995... 

Figure C2.10.3. Ex situ investigation of the electrochemical double layer on Ag after hydrophobic emersion from 1 M NaClO + 0.1 M NaOH. (a) Peak deconvolution of the XPS 01s signals after emersion at +0.2 V A surface...

Hendler R W and Shrager R I 1994 Deconvolutions based on singular value decomposition and the pseudoinverse—a guide for beginners J. Blochem. Blophys. Methods 28 1-33... 

The major impetus for the development of solid phase synthesis centers around applications in combinatorial chemistry. The notion that new drug leads and catalysts can be discovered in a high tiuoughput fashion has been demonstrated many times over as is evidenced from the number of publications that have arisen (see references at the end of this chapter). A number of )proaches to combinatorial chemistry exist. These include the split-mix method, serial techniques and parallel methods to generate libraries of compounds. The advances in combinatorial chemistry are also accompani by sophisticated methods in deconvolution and identification of compounds from libraries. In a number of cases, innovative hardware and software has been developed tor these purposes. 

Most EDS systems are controlled by minicomputers or microcomputers and are easy to use for the basic operations of spectrum collection and peak identification, even for the computer illiterate. However, the use of advanced analysis techniques, including deconvolution of overlapped peaks, background subtraction, and quantitative analysis will require some extra training, which usually is provided at installation or available at special schools. 

The characteristic peaks must be deconvolved to eliminate peak interference powerful deconvolution algorithms exist for EDS and WDS. 

Figure 2.36 A shows a typical low-loss spectrum taken from boron nitride (BN). The structure of BN is similar to that of graphite, i. e. sp -hybridized carbon. For this reason the low-loss features are quite similar and comprise a distinct plasmon peak at approximately 27 eV attributed to collective excitations of both n and a electrons, whereas the small peak at 7 eV comes from n electrons only. Besides the original spectrum the zero-loss peak and the low-loss part derived by deconvolution are also drawn. By calculating the ratio of the signal intensities hot and Iq a relative specimen thickness t/2 pi of approximately unity was found. Owing to this specimen thickness there is slight indication of a second plasmon.

Metrology and contamination analysis in particular have been decisive factors for profitable semiconductor production [4.47]. Semiconductor applications of TXRF go back to the late nineteen-eighties and were introduced by Eichinger et al. [4.48, 4.49]. Because of its high sensitivity, wide linear range, facile spectrum deconvolution, and... 

It is seen that the two curves are quite different and, if the results are fitted to the HETP equation, only the data obtained by using the exit velocity gives correct and realistic values for the individual dispersion processes. This point is emphasized by the graphs shown in Figure 5 where the HETP curve obtained by using average velocity data are deconvoluted into the individual contributions from the different dispersion processes. 

It is evident from the exceptions noted that the mechanism proposed above does not fully capture the pathways open to the Patemo-Biichi reaction. A great deal of effort has been devoted to deconvoluting all of the possible variants of the reaction. Reactions via singlet state carbonyls, charge-transfer paths, pre-singlet exciplexes, and full electron transfer paths have all been proposed. Unfortunately, their influence on product... 

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