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Signal, Image and Video Processing

, Volume 9, Issue 4, pp 801–807 | Cite as

Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

  • Erdal Dinç
  • Fernando B. Duarte
  • J. A. Tenreiro MachadoEmail author
  • Dumitru Baleanu
Original Paper

Abstract

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter \(a\) of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Keywords

Fractional Fourier transform  Continuous wavelet transform Spectral resolution Quantitative analysis Binary mixture 

Notes

Acknowledgments

This work was done within the Chemometric Laboratory of Faculty of Pharmacy, and it was supported by the scientific research project No. 10A3336001 of Ankara University, Turkey.

References

  1. 1.
    Gunes, V., Inci, A., Uyanik, F., Yildirim, A., Altug, N., Eren, M., Onmaz, A.C., Gelfert, C.C.: The effect of oxfendazole plus oxyclozanide paste and tablet formulations on parasite burden and metabolic status of sheep. J. Animal Vet. Adv. 5(7), 589–594 (2008)Google Scholar
  2. 2.
    Dinç, E., Baleanu, D., Tokar, F.: Simple mathematical resolution for binary mixture of oxfendazole and oxyclozanide in bolus by bivariate and multivariate calibrations based on the linear regression functions. Revue Roumaine de Chimie 4(53), 303–307 (2008)Google Scholar
  3. 3.
    Dinç, E., Baleanu, D.: Continuous wavelet transform applied to the overlapping absorption signals and their ratio signals for the quantitative resolution of mixture of oxfendazole and oxyclozanide in bolus. J. Food Drug Anal. 2(15), 109–117 (2007)Google Scholar
  4. 4.
    Dinç, E., Kanbur, M.: Spectrophotometric multicomponent resolution of a veterinary formulation containing oxfendazole and oxyclozanide by multivariate calibration-prediction techniques. J. Pharm. Biomed. Anal. 3–4(28), 779–788 (2002)CrossRefGoogle Scholar
  5. 5.
    Khan, A.R., Akhtar, M.J., Mahmood, R., Ahmed, S.M., Malook, S., Iqbal, M.: LC assay method for oxfendazole and oxyclozanide in pharmaceutical preparation. J. Pharm. Biomed. Anal. 1(22), 111–114 (2000)CrossRefGoogle Scholar
  6. 6.
    Dinç, E., Onur, F.: Comparative study of the ratio spectra derivative spectrophotometry, derivative spectrophotometry and Vierordt’s method applied to the analysis of oxfendazole and oxyclozanide in a veterinary formulation. Analysis 3(25), 55–59 (1997)Google Scholar
  7. 7.
    Condom, E.U.: Immersion of the Fourier transform in a continuous group of functional transformations. Proc. Natl. Acad. Sci. 3(23), 158–164 (1937)CrossRefGoogle Scholar
  8. 8.
    Ozaktas, H.M., Ankan, O., Kutay, M.A., Bozdaği, G.: Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 44(9), 2141–2150 (1996)CrossRefGoogle Scholar
  9. 9.
    Tao, R., Deng, B., Zhang, W.-Q., Wang, Y.: Sampling and sampling rate conversion of band limited signals in the fractional Fourier transform domain. IEEE Trans. Signal Process. 56(1), 158–171 (2008)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Ozaktas, H.M., Zalesvsky, Z., Kutay, M.A.: The Fractional Fourier Transform. Wiley, Chichester (2001)Google Scholar
  11. 11.
    Narayanan, V.A., Prabhu, K.M.M.: The fractional Fourier transform: theory, implementation and error analysis. Microprocess. Microsyst. 27(10), 511–521 (2003)CrossRefGoogle Scholar
  12. 12.
    Bultheel, A., Martínez Sulbaran, H.: Computation of the fractional Fourier transform. Appl. Comput. Harmon. Anal. 16(3), 182–202 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Campos, R.G., Rico-Melgoza, J., Chavez, E.: XFT: extending the digital application of the Fourier transform. http://www.citebase.org/abstract?id=oai:arXiv.org:0911.0952
  14. 14.
    Saxena, R., Singh, K.: Fractional Fourier transform: a novel tool for signal processing. J. Indian Inst. Sci. 85, 11–26 (2005) Google Scholar
  15. 15.
    Pei, S.-C., Ding, J.-J.: Relations between Gabor transforms and fractional Fourier transforms and their applications for signal processing. IEEE Trans. Signal Process. 55(10), 4839–4850 (2007)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Erdal Dinç
    • 1
  • Fernando B. Duarte
    • 3
  • J. A. Tenreiro Machado
    • 2
    Email author
  • Dumitru Baleanu
    • 4
    • 5
    • 6
  1. 1.Department of Analytical Chemistry, Faculty of PharmacyAnkara UniversityAnkaraTurkey
  2. 2.Department of Electrical EngineeringInstitute of Engineering, Polytechnic of PortoPortoPortugal
  3. 3.Faculty of Engineering and Natural SciencesLusofona UniversityLisbonPortugal
  4. 4.Department of Mathematics and Computer Sciences, Faculty of Arts and SciencesÇankaya UniversityAnkaraTurkey
  5. 5.National Institute for Laser, Plasma and RadiationInstitute of Space SciencesMagurele-BucharestRomania
  6. 6.Department of Chemical and Materials Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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