### Contact Info

Stuart Chalk, Ph.D.

Department of Chemistry

University of North Florida

Phone: 1-904-620-1938

Fax: 1-904-620-3535

Email: schalk@unf.edu

Website: @unf

## Fourier transform

### Citations 12

**"Shah Convolution Differentiation Fourier Transform For Rear Analysis In Microchip Capillary Electrophoresis"**

*J. Chromatogr. A
2001 Volume 924, Issue 1-2 Pages 177-186*

Yien C. Kwok and Andreas Manz

**Abstract:**This paper first reports the application of Shah convolution differentiation Fourier transform for rear analysis. Rear analysis eliminates the need to create a well-defined and reproducible sample plug, thus making the operation simpler. The number of solution reservoirs, for microchip capillary electrophoresis (CE), could be reduced from the usual four to three. Sample bias in CE could be avoided too. The separation channel was first filled with the fluorescent sample solution, and subsequently flushed out with the buffer. The rear of each analyte zone gives rise to its flight of sigmoid-shaped steps in the time-domain. The time-domain detector signal was first differentiated and then Fourier transform was performed. The Fourier transform results were represented in the form of a magnitude plot. It is proposed that this would be as equally applicable to other separation techniques (e.g., chromatography) and detection methods (e.g., absorption). (C) 2001 Elsevier Science BV All rights reserved.

**"Impulse/response Functions Of Individual Components Of Flow Injection Manifolds"**

*Anal. Chim. Acta
1988 Volume 214, Issue 1-2 Pages 77-86*

I. C. van Nugteren-Osinga, M. Bos and W. E. van der Linden

**Abstract:**Mathematical deconvolution is applied to evaluate the impulse/response functions of the individual parts of a flow injection manifold system. A fast Fourier transform algorithm was used. The results enable prediction of performance of other modular arrangements of such parts.

**"Impulse/response Functions Of Individual Components Of Flow Injection Manifolds"**

*Anal. Chim. Acta
1988 Volume 214, Issue 1-2 Pages 77-86*

I. C. van Nugteren-Osinga, M. Bos and W. E. van der Linden

**Abstract:**Mathematical deconvolution is applied to evaluate the impulse/response functions of the individual parts of a flow injection manifold system. A fast Fourier transform algorithm was used. The results enable prediction of performance of other modular arrangements of such parts.

**"Signal Filtering Of Potentiometric Stripping Analysis Using Fourier Techniques"**

*Anal. Chim. Acta
1997 Volume 338, Issue 3 Pages 167-178*

C. W. K. Chow*, D. E. Davey and D. E. Mulcahy

**Abstract:**Four filtering functions, rectangular, triangular, exponential and decay exponential for Fourier filtering have been compared in this study of potentiometric stripping analysis (PSA) data. The filtering procedure involves treating the potential coordinate as mathematically equivalent to a time coordinate to transform data to the frequency domain. After Fourier transformation, each method yielded signal-to-noise enhancement over the original data in the order, decay exponential>triangular>exponential>rectangular. Apart from the filtering functions, two different filtering procedures, conventional and reflectance, have been compared in this study. Peak area measurement was unaffected by the reflectance procedure, while an undesirable increase in peak area was observed in the conventional procedure. A linear peak area-concentration relationship was retained in all cases. The resolution of overlapping potential peaks, using copper and bismuth peaks as the example, was most improved using the rectangular filtering function and worst using the decay exponential filtering function. This is completely opposite to the results obtained in signal-to-noise enhancement study. Thus, a compromise between SIN ratio enhancement and peak distortion has to be made, as the latter is always a trade-off in signal processing. With the use of a personal computer (PC) and commercial data acquisition systems, the original saved data can be stored. Selection of a particular type of filtering function to optimise the analytical signal can be achieved by applying various functions to the original signal, until a desirable output is obtained. 22 References

**"Automated Flow Injection Spectrophotometric Non-aqueous Titrimetric Determination Of The Free Fatty-acid Content Of Olive Oil"**

*Anal. Chim. Acta
1997 Volume 351, Issue 1-3 Pages 291-297*

Panayotis G. Nouros, Constantinos A. Georgiou and Moschos G. Polissiou*

**Abstract:**An automated how injection titrimetric method for the determination of olive oil acidity is proposed. A 175 µl olive oil aliquot is injected in a carrier stream (the titrant) of n-propanol containing 7.5 x 10^-4 M KOH and 4.0 x 10^-5 M phenolphthalein indicator. The sample zone is dispersed in the titrant while flowing at 4.4 mi min-1 through a 1.1 mi Plexiglas mixing chamber and the absorbance of the resulting mixture is continuously monitored at 562 nm, lambda(max), for the basic form of the indicator. The resulting negative absorbance peaks indicate the transition base (red)-acid (colorless)-base (red) of the indicator. Quantitation is based on peak width measurements. Peak widths of 31.7-97 a were measured with a relative standard deviation (RSD) of < 2.1% (n = 10), and the analytical range was 0.15-8.0% (w/w) free fatty acid content calculated as oleic acid. The sampling rate is 30-100 h-1 while n-propanol consumption is only 3-7 mi per run. Recoveries of oleic acid from commercial olive oils ranged from 97.9 to 101.6% (mean 99.5%). The method was applied for the determination of free fatty acid content of thirty two samples of olive oils. Results obtained by the proposed method compare well (0.3-3.6% relative difference, mean 1.5%) with those obtained by the official European Community method that is time consuming and uses gross amounts of organic solvents. Moreover comparison with a Fourier transform infrared F-IR) method reveals that by using the proposed method the useful range can be extended to lower concentrations. 18 References

**"Deconvolution Techniques For Rapid Flow Injection Analysis"**

*Talanta
1985 Volume 32, Issue 8B Pages 807-810*

James T. Dyke and Quintus Fernando*

**Abstract:**Techniques of FT deconvolution and of iterative-convolution curve-fitting (Vanderslice et al., Ibid., 1981, 28, 11) were investigated, the variables being the effect of random noise and the signal-to-noise ratio. Use of these techniques in spectrophotometric flow injection analysis to separate overlapping peaks permits the sampling rates to be increased. The iterative method is less sensitive to random noise than is FT deconvolution.

**"The Electronic Toolbox. 2"**

*Anal. Chem.
1985 Volume 57, Issue 12 Pages 1298A-1314A*

Raymond E. Dessy

**Abstract:**Integrated circuits can provide specific functions for operations such as Fourier transform, filtering, correlation and convolution. Detector arrays and non-specific sensors are available for rapid collection and resolution of spectra, measurement of particle size and distribution and the monitoring of atmospheres for hazardous components. An example for the use of self-optimizing instruments involves the establishment of conditions for flow injection analysis.

**"Generalized Fourier Smoothing Of Flow Injection Analysis Data"**

*Anal. Chem.
1994 Volume 66, Issue 24 Pages 4507-4513*

Oliver Lee, Adrian P. Wade, and Guy A. Dumont

**Abstract:**The Fourier transform is widely used for smoothing data such as those from flow injection analysis (FIA). The effectiveness of this method can be enhanced if, in addition to the standard complex exponential functions, the Fourier transform is generalized to use other sets of complete, orthogonal functions such as the Gram or Meixner polynomials as its basis functions. The choice of which set of basis functions to use depends on its efficiency on a given peak. Using simulated noisy FIA peaks differing in degree of skewness, it was found that the standard complex exponential set is best-suited for symmetric or nearly symmetric peaks, and the Meixner set, for moderate to greatly skewed peaks. The Gram set weakly favors skewed peaks, but it is not more effective than both the complex exponential and Meixner sets over any portion of the skewness range studied. The problem of determining the optimal spectral cutoff point was cast in terms of hierarchical model selection, and a generalized Akaike information-theoretic criterion (GAIC) was evaluated for its ability to find the best filter order. Use of an efficient basis minimizes the chance of selecting a non-optimal filter order. The combination of generalized Fourier filtering and the GAIC provides an attractive means to filter FIA data automatically.

**"Cross-correlation With Digital Techniques In Flow Injection Analysis And High Performance Liquid Chromatography"**

*Electroanalysis
1992 Volume 4, Issue 4 Pages 495-500*

D. J. Curran, R. E. McKeans

**Abstract:**Digital signal processing techniques were applied in demonstrating the use of cross-correlation procedures in order to improve the signal-to-noise ratio in measurements involving analogue detectors in flowing streams. Two examples of the technique are presented as illustrations. The first involves the amperometric detection of dopamine in a flow injection procedure wherein the reference and analyte signals are digitized and cross-correlation performed by software using the fast FT technique. The second example concerns the HPLC analysis of a mixture of norepinephrine, L-dopa, dopamine (I) and epinephrine (II) on an Adsorbosphere C-18 column (15 cm x 4.6 mm) with methanol - 0.05 M phosphate buffer (8:92; pH 3.4) and UV detection at 280 nm. In this instance the signals from the UV detector were cross-correlated by multiplying a digitized reference chromatogram by the digitized analysis chromatogram and performing low pass filtering in the digital domain. The signal-to-noise ratio was improved by factors of 15 and 35 for I and II, respectively. Digital techniques are implemented to demonstrate the use of cross correlation to improve the signal-to-noise ratio for measurements involving analog detectors in flowing stream anal. methods. Two examples are presented. The first involves amperometric detection of dopamine using flow injection analysis. The reference and analyte signals are digitized and cross correlation performed by software using the fast Fourier transform (FFT). The second example is the determination of a mixture of catecholamines by HPLC using a UV detector. Multiplication of the digitize reference and analyte signals was carried out in the time domain followed by low pass filtering. Improvement in the signal-to-noise ratio up to a factor of 35 was found, depending on the compound

**"Peristaltic Pumps - Fourier Transforms: A Coupling Of Interest In Continuous-flow Flame Atomic Absorption Spectrometry"**

*Spectrochim. Acta B
1996 Volume 51, Issue 14 Pages 1761-1768*

I. López-García, M. Sánchez-Merlos, P. Viñas and M. Hernández-Córdoba*

**Abstract:**The modulation imposed by the peristaltic pulses is Fourier-transformed into a frequency spectrum; the amplitude observable at the known pulse frequency can then be distinguished from noise signals. The module of the signal at a frequency of nomega/60 can be used as the analytical signal to lower the limit of determination by a factor of 5-6 with respect to that obtainable by aspiration. Concentrations that are too high to be measured with direct aspiration can be measured by including an auxiliary channel in the manifold to compensate for the difference between the pumping rate and the nebulizer uptake rate and using the amplitude as the analytical signal. Only a single standard solution analyzed under different conditions is required for calibration.

**"A Computational Technique For Simulating The Dynamic Response Of A Flow Injection Analysis System"**

*Chem. Eng. Sci.
1992 Volume 47, Issue 7 Pages 1591-1600*

Steven H. Isaacs and Henrik Soeberg, Lars H. Christensen and John Villadsen

**Abstract:**A computational technique is presented for obtaining the dynamic response to a gas diffusion module as part of a flow injection analysis (FIA) system. Based on orthogonal collocation, Laplace transformation, and Fourier series, the method provides a relatively quick way to account for dispersive effects occurring via longitudinal convection and lateral diffusion. Simulation examples, including a comparison with a dynamic signal obtained with an actual FIA system, are provided.

**"Direct Analysis Of Organic-compounds In Water By Membrane Introduction Mass-spectrometry Advances In Selectivity And Interfaces"**

*Process Control Qual.
1995 Volume 7, Issue 3-4 Pages 117-131*

J.S. Patrick, P. Wong, C. Xu, M. Soni, N. Kasthurikrishnan, N. Srinivasan and R.G. Cooks

**Abstract:**An overview of recent advances in membrane introduction mass spectrometry (MIMS) is presented. Particular attention is given to developments in interfaces, improvements in sensitivity and enhancements in selectivity. A new interface is employed which uses pneumatically assisted transport of the analyte to a jet separator interfaced to a benchtop ion trap mass spectrometer. Affinity MIMS, a new experiment which allows selective trapping of analytes (here benzaldehydes) at a chemically modified membrane, is described. Extended loading times followed by release using a chemical agent yields a limit of detection of 10 ppb for benzaldehyde. Notched broad-band excitation using stored waveform inverse Fourier transform (SWIFT) experiments on a benchtop ion trap is also used to enhance selectivity by permitting injection or retention of selected ions within the ion trap. The combination of SWIFT, signal averaging and extended ionization times has allowed the detection of trans-dichloroethene and toluene at 500 parts-per-quadrillion levels in water with no sample pre-concentration. Tandem mass spectrometry of analytes, introduced by MIMS, is also performed using SWIFT on the benchtop ion trap instrument. Both unimolecular dissociations and ion/molecule reactions can be used to characterize analytes. Trace level(10 ppb) analysis of volatile organics in a seawater matrix is described using flow injection sample handling; the matrix causes no changes in permeation rate or detector response relative to an aqueous solution. Methods are discussed for the detection of glycerol and 5-hydroxymethylfurfuraldehyde, a dehydration product of glucose, using MIMS. Finally, information acquired by MIMS is used to provide feedback control of a yeast fermentation. Each of these advances in MIMS finds application in online monitoring of chemical process streams. (52 references)