Spectral subtraction

If a spectrum is linear in absorbance, the spectrum can be scaled to represent the sample at a different concentration or pathlength, within certain limitations. If the factor by which the spectrum is scaled is too large, the absorbances will extend to unreasonable values. If a linear spectrum is scaled to very high absorbance values, the lineshapes will not match measured spectra as all subtractions fail at sufficiently high absorbances. Consequently, a spectrum scaled to very high absorbance is unrealistic. Nonetheless, if two spectra are of the same sample and are both linear 

Subtraction can be used to verify the identity of a sample. If a spectrum of a known compound is subtracted from a spectrum of what appears to be the same compound, and a zero residual results, the samples are identical. This is a useful tool for verification and should be used to validate identification after hbrary searching (see Section 10.8). 

Artifacts, or errors, are frequently observed in difference spectra. If the minuend and subtrahend spectra have shifted wavenumber scales with respect to each other. 

It is not always the case that the minuend and the subtrahend will have the same lineshapes, in that the spectra may have been calculated with different apodization functions (something that should be avoided whenever possible), or the same line-shape may be distorted because of different concentrations. Differences in line-shape will often be exhibited as differences in bandwidth. If the minuend spectrum has bands that are broader than the subtrahend, even when the peak absorbances are matched, the difference spectrum will contain small doublets. The existence of these doublets is often taken as evidence of a minor component in the minuend, but in reality these are rarely more than subtraction artifacts. This phenomenon is generally more apparent when broad bands are subtracted. 

It is not always possible to perform a good spectral subtraction, as the minuend spectram may be unavoidably nonlinear. (Generally, it is assumed that a reference spectrum, i.e., the subtrahend, will be linear if it is a good reference.) If the subtrahend can be remeasured under the same nonlinear conditions as the minuend, the nonlinearities should be sufficiently similar to effect a valid subtraction. In this case the scaling factor approaches unity, and reliable subtraction may be possible. 

Rule 4 tells you to show your work. The information to record includes who did the processing, when it was performed, what software brand and version number was used, what algorithm and parameters were used, and why the manipulation was performed. This data can be written on a hard copy of the spectrum, recorded in a lab notebook, or saved in electronic form. Some software packages record some or all of this information for you automatically. What matters is that this information be recorded because processing a spectrum can alter its appearance, and anyone who looks at a spectrum needs to know what was done so they can take it into account when interpreting the spectrum. Also, publishing a processed spectrum without stating how and why it was processed is a form of scientific fraud—a behavior best avoided if you value your career. 

The purpose of these rules is not to scare you away from using spectral processing, but to encourage you to use these algorithms properly so you can enjoy their benefits. 

FIGURE 3.1 An example of a spectral subtraction. The sample spectrum displayed at the bottom is of the amino acid glutamine dissolved in water. The reference spectrum shown in the middle is of pure liquid water. The top spectrum is of the subtraction result. 

For subtraction to work properly the two spectra must be plotted with y-axis units that are linearly proportional to concentration, such as absorbance. Single beam spectra or spectra plotted in percent transmittance have peak sizes that are not linear with concentration and should not be used in spectral subtraction. The mathematical algorithm behind spectral subtraction is relatively simple and is given by Equation 3.1  

This equation states that the absorbance at a given wavennmber in the resnlt is eqnal to the difference in absorbance between the sample and reference spectmm at that wavenumber. For example, if the absorbance of the sample spectrum at 3000 cm is 0.5, and the absorbance of the reference spectrum at 3000 cm is 0.2, the result absorbance will be 0.3. A subtraction result then is a plot of the difference in absorbance between the sample and reference spectra plotted versus wavenumber. 

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Nonnal spontaneous Raman scahering suffers from lack of frequency precision and thus good spectral subtractions are not possible. Another limitation to this technique is that high resolution experiments are often difficult to perfomi [39]. These shortcomings have been circumvented by the development of Fourier transfomi (FT) Raman spectroscopy [40]. FT Raman spectroscopy employs a long wavelength laser to achieve viable interferometry. 

Simulated spectra can be created by another option in the main menu of the program. Probabilities (P1-P4) are prompted from the user, depending on the model, if vaiues other than those stored with the data base are desired and a single linewidth is entered. Equation 1 and 2 are then used to simulate a spectrum which can be saved, compared to the experimental spectrum (including overlaying spectra, spectral subtractions, additions, etc.) or plotted. 

Mrad/h). Films were stored at -20° until analysis could be carried out. Oxidized films and derivatized, oxidized films were characterized by iodometry (reflux with Nal in isopropanol/acetic acid) and by transmission Fourier Transform (FT) IR (Perkin Elmer 1500), using the spectral subtraction technique (3, 14). Free radicals were measured by the electron spin resonance technique (e.s.r., Varian E4 spectrometer). 

Derrick studied the interaction of L-tryptophan and ibuprofen with human serum albumin (HSA),74 which is an abundant transport blood protein capable of binding efficiently several species.75 They acquired 1H NMR spectra of L-Tryptophan-HSA system for different ligand protein molar ratios, that is 3 1, 5 1, 7 1 and 10 1. The aromatic resonances of L-Tryptophan are difficult to be observed due to the overlap with HSA signals, even at 10 1 molar ratio, so that the spectral subtraction was performed. D values of L-Tryptophan were calculated by integration of the subtracted spectra and were in good agreement with those predicted by computer simulations. In the case of ibuprofen, only for 140 1 molar ratio, the resonances of ibuprofen are clearly visible also in this case, the... 

Selecting an approach Physical separation of the two compounds will not be easy, but mass spectral subtraction techniques may allow you to obtain a spectrum of the peak of interest. 

Fig. 21.11. Mass spectra of the unknown off-flavor compound after spectral subtraction from the co-eluting peak and the matching spectrum from the NIST library. (Redrawn/redrawn from J. Chromatogr., 351, R.A. Sanders, and T.R. Morsch, Ion profiling approach to detailed mixture comparison. Application to a polypropylene off-odor problem, 525-531, Copyright (1986) with permission from Elsevier.)...

The IR methods have progressed from hand-drawn baselines and peak height or area for quantitation, to spectral subtraction, to leastsquares methods. Least-squares analysis eliminates the reliance on single peaks for quantitation and the subjectivity of spectral subtraction. However, negative concentration coefficients are a problem with least-squares analysis, since they have no physical meaning. Negative components can be omitted according to some criterion and the least-squares process iterated until only... 

Spectral subtraction usually provides a sensitive method for detecting small changes in the sample. Figure 5 shows the difference spectra between the atactic poly(a,a-dimethylbenzyl methacrylate) s unexposed and exposed to electron-beam at several doses. The positive absorption at 1729 cm-1 is due to the ester carbonyl group consumed on the exposure and the negative ones at 1700 and 1760 cm-1 to the acid and acid anhydride carbonyl groups formed, respectively. The formation of methacrylic acid units was more easily detected using the difference spectrum However, these difference spectra could not be used for the quantitative determination because the absorptions overlap somewhat. 

Mechanical deformation induces orientation into the polymer samples and polarized infrared can be used to characterize this orientation either by direct measurement of the dichroic ratio 287,289) or by spectral subtraction 286), three dimensional sample tilting 68,286), or internal reflection spectroscopy 130). 

ATR spectroscopy in the infrared has been used extensively in protein adsorption studies. Transmission IR spectra of a protein contain a wealth of conformational information. ATR-IR spectroscopy has been used to study protein adsorption from whole, flowing blood ex vivo 164). Fourier transform (FT) infrared spectra (ATR-FTIR) can be collected each 5-10 seconds165), thus making kinetic study of protein adsorption by IR possible 166). Interaction of protein with soft contact lens materials has been studied by ATR-FTIR 167). The ATR-IR method suffers from problems similar to TIRF there is no direct quantitation of the amount of protein adsorbed, although a scheme similar to the one used for intrinsic TIRF has been proposed 168) the depth of penetration is usually much larger than in any other evanescent method, i.e. up to 1000 nm water absorbs strongly in the infrared and can overwhelm the protein signal, even with spectral subtraction applied. 

Standard examples of noise-suppression rules include the so-called Wienei6 suppression rule, the power-subtraction (see Figure 4.16), the spectral subtraction [Boll, 1979, Lim and Oppenheim, 1979, McAulay and Malpass, 1980, Vary, 1985], as well as several families of parametric suppression curves [Lim and Oppenheim, 1979, Moorer and Berger, 1986, Etter and Moschytz, 1994],... 

These techniques are also often referred to as "spectral subtraction . We will not use this terminology in order to avoid ambiguities between the general principle and the particular technique described in [Boll, 1979], nor will we use the term spectral estimation as quite a number of the STSA techniques are not based on a statistical estimation approach. 

Block diagram of a spectral-subtraction noise-reduction system. 265... 

A variant on spectral subtraction is the INTEL technique [Weiss et al., 1975], in which the square root of the magnitude spectrum is computed and the rooted spectrum is then further transformed via a second FFT. Processing similar to that described above is then performed in this pseudo-cepstral domain. The estimate of the speech amplitude function in this domain is transformed back to the magnitude spectral domain and squared to remove the effect of rooting the spectrum. 

Boll, 1979] Boll, S. F. (1979). Suppression of acoustic noise in speech using spectral subtraction. IEEE Trans. Acoust., Speech, Signal Processing, 27(2) 113-120. 

Spectral subtraction can also be used to enhance the more subtle differences between two samples by the nulling of spectral features common to two spectra, which leaves the differences between samples as excursions from an otherwise featureless baseline. Interpretation of such difference spectra is usually done in conjunction with measurement of other spectroscopic changes, such as band shifts or intensity changes, that are produced in a series of spectra of a bulk phase sample perturbed in some manner. Examples will be discussed further below in the various subsections. 

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