Effect of the sampling matrix

This inserts zero values at the e-vertex positions and doubles whatever values were originally present to give v-vertices. 

If the original polygon is sampled from a sinusoid of spatial frequency ui = 1/m where m is the number of polygon points per complete cycle, so that P0[j] = cos(2njcj), j G Z, the result of multiplying by the sampling matrix can be expressed as 

We can view this as the sum of a signal component, cos(2njcj), and an artifact component30, cos(2irju )cos(2nj) 

29Strictly speaking the rows are the reverse of the mask, but because we deal with palindromic masks we ignore that here. 

30This can further be expressed in terms of two sideband components, cos 2 k lo 1 )j), but for this analysis it is convenient not to do so. 

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Satow, T., Machida, A., Funakushi, K., and Palmieri, R., Effects of the sample matrix on the separation of peptides by high performance capillary electrophoresis, HRC CC, 14, 276, 1991. 

Smith and Udseth [154] first described SFE-MS in 1983. Direct fluid injection (DFT) mass spectrometry (DFT-MS, DFI-MS/MS) utilises supercritical fluids for solvation and transfer of materials to a mass-spectrometer chemical ionisation (Cl) source. Extraction with scC02 is compatible with a variety of Cl reagents, which allow a sensitive and selective means for ionising the solute classes of interest. If the interfering effects of the sample matrix cannot be overcome by selective ionisation, techniques based on tandem mass spectrometry can be used [7]. In these cases, a cheaper and more attractive alternative is often to perform some form of chromatography between extraction and detection. In SFE-MS, on-line fractionation using pressure can be used to control SCF solubility to a limited extent. The main features of on-line SFE-MS are summarised in Table 7.20. It appears that the direct introduction into a mass spectrometer of analytes dissolved in supercritical fluids without on-line chromatography has not actively been pursued. 

Employing the method known as multiple standard addition helps when trying to discern the effects of the sample matrix in which an analyte is dissolved. In this technique, the emf is determined as a function of the amount of standard solution added to the sample. 

A study to explore the effect of the sample matrix in SFE was done with a set of polychlorinated biphenyl (PCBs) and a river sediment matrix. Figure 12 shows the on-line SFE/GC characterization of a PCB standard ranging from monochloro to decachlorolbiphenyl compounds present at concentration levels from 5 to 100 microgram per milliliter. An election capture GC detector (ECD) was used for the determination of these PCB s. Since this PCB standard was made up in liquid... 

Fu I, Woolf EJ, Matuszewski BK (1998) Effect of the sample matrix on the determination of indinavir in human urine by HPLC with turbo ion spray tandem mass spectrometric detection. J Pharm Biomed Anal 18 347-357... 

Molecular absorption interferences can be reduced considerably by ashing within the atomiser itself, although care must be taken to avoid preatomisation losses of lead which occur at 350—400°C with untreated blood samples. These losses may be avoided at higher temperatures by the addition of a solution of (NH4)2HP04 [111]. The net effect of the sample matrix on... 

Sample blanks are samples that are used to establish the effect of the sample matrix or to ensure that the matrix is not affecting the analysis. They approximate to the analytical samples except that they do not contain any measurable concentration of the analyte under investigation. 

Fu, L Woolf, E.J. Matuszewski, B.K. "Effect of the Sample Matrix on the Determination of Indinavir in Human Urine by HPLC with Turbo Ion Spray Tandem Mass Spectrometric Detection," J. Pharm. Biomed. Anal. 18, 347-357 (1998). 

Matrix Spike Standard consists of a representative set of the targeted analytes whose percent recoveries are evaluated in the sample matrix. For example, if THMs were the targeted analytes, this reference standard would consist of one or more THMs such as chloroform, bromodichloromethane, and chlorodibromomethane. These compounds would be dissolved in a matrix-compatible solvent such as MeOH. A precise aliquot of this solution is added to a sample so that the effect of the sample matrix on the percent recovery can be evaluated. A second standard called a matrix spike duplicate is often required in EPA methods and is used to assess matrix recovery precision. 

Few comprehensive studies have been published on the effect of the sample matrix on the partitioning of VOCs at trace concentration levels. 

Matrix spike standard Consists of a representative set of the targeted analytes (i.e., OCs and/or PCBs dissolved in MeOH). A precise aliquot of this solution is added to a sample so that the effect of the sample matrix on the percent recovery can be evaluated. 

In order to obtain quantitative results by HS-GC, the system must be calibrated. Absolute quantitation is not possible. Quantification can be done by the conventional external calibration method with liquids containing the analytes concerned in known concentrations or by means of standard addition. Pausch et al. [958] have developed an internal standard method for solid headspace analysis of residuals in polymers in order to overcome the limitations of external standardisation cfr. Chp. 4.2.2 of ref. [213a]). Use of an internal standard works quite well, as shown in case of the determination of residual hydrocarbon solvent in poly(acrylic acid) using the solid HS-GC-FID approach [959]. In the comparison made by Lattimer et al. [959] the concentrations determined by solid HS-GC exceeded those from either solution GC or extraction UV methods. Solid HS-GC-FID allows sub-ppm detection. For quantitative analysis, both in equilibrium and non-equilibrium conditions, cfr. ref. [960]. Multiple headspace extraction (MHE) has the advantage that by extracting the whole amount of the analyte, any effect of the sample matrix is eliminated the technique is normally used only for method development and validation. 

Effect of the sample s matrix on a normal calibration curve. 

A particular issue that must be considered for all calibration procedures is the possibility of matrix effects on the analyte signal. If such effects are present they may be allowed for in many cases by matrix matching of the standard to the sample. This of course requires an accurate knowledge of the sample matrix. Where this is not available, the method of standard addition is often effective. This involves spiking at least three equal aliquots of the sample with different amounts of the analyte, and then measuring the response for both spiked and unspiked aliquots. A plot of response vs analyte, extrapolated back, will give abscissae intercepts from which the amount of analyte in the sample may be deduced (Figure 2.8). 

Primary calibration with increasing weights of oil is the most accessible, because new calibration standards can easily be reproduced as long as representative seed oil is available however, this calibration does not take into consideration the effect of the seed matrix on the NMR signal of the oil, and therefore may not be entirely accurate. Also, the stability of extracted oil may be somewhat more poor than in the intact oilseed. Freshly extracted oil should be used to ensure a representative sample. 

The Raman effect has also been broadly applied to online and bench-top quantitative applications, such as determination of pharmaceutical materials and process monitoring [4-6], in vivo clinical measurements [7], biological materials [8, 9], to name only a few. Because the absolute Raman response is difficult to measure accurately (sample presentation and delivered laser power can vary), these measurements are almost always calculated as a percentage with respect to the response from an internal standard. This standard is typically part of the sample matrix in a drug product, the standard may be an excipient in a biological sample, it is commonly water. 

Although the problem of oxide formation is greatly reduced in GFAA analysis because atomization occurs in an inert atmosphere, the technique is nevertheless susceptible to chemical interferences. The chemical composition of the sample matrix can have a major effect on the analysis, and the magnitude of this effect must be determined and taken into consideration in the analysis of each new, unknown or a particularly complex matrix. 

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