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


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.


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



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.


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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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