zbMATH — the first resource for mathematics

Fractional wavelet transform for the quantitative spectral resolution of the composite signals of the active compounds in a two-component mixture. (English) Zbl 1189.94028
Summary: Fractional calculus is a powerful tool that has been applied successfully for the analysis of the complex systems. One interesting example of a complex mixture is given by the multicomponent pharmaceutical samples having constant matrix content. The main aim of this study is to develop a new approach based on the combined use of the fractional wavelet transform (FWT) and the continuous wavelet transform (CWT) in order to quantify atorvastatin (ATO) and amlodipine (AML) in their mixtures without requiring a chemical pretreatment. In the first step, the absorption spectra of the compounds and their samples were processed by the FWT method. In the next step, the CWT approach was applied to the fractional wavelet spectra obtained in the above step. The aim of the application of FWT is data reduction corresponding to the spectra of compounds and their commercial samples. In the following step, the CWT was used for the quantitative resolution of the composite signals of the analyzed compounds. After method validation, the proposed signal processing methods based on the combined use of the FWT and the CWT were successfully applied to the resolution of the composite spectra for the quantitation of atorvastatin (ATO) and amlodipine (AML) in tablets.

94A11 Application of orthogonal and other special functions
Full Text: DOI
[1] T. Blu, M. Unser, The fractional spline wavelet transform: Definition and implementation, in: Proceedings of the Twenty-Fifth IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP’00, Istanbul, Turkey, June 5-9, vol. I, 2000, pp. 512-515
[2] Blu, T.; Unser, M., IEEE trans. signal process., 50, 3, 543-553, (2002)
[3] M. Unser, T. Blu, Construction of fractional spline wavelet bases, in: Proc. SPIE Wavelets Applications in Signal and Image Processing VII, Denver, CO, 3813, 1999, pp. 422-431
[4] Unser, M.; Blu, T., Fractional splines and wavelets, SIAM rev., 42, 1, 43-67, (2000) · Zbl 0940.41004
[5] Daubechies, I., Ten lectures on wavelets, (1992), Society for Industrial and Applied Mathematics Philadelphia · Zbl 0776.42018
[6] Walczak, B., Wavelets in chemistry, (2000), Elsevier Press Amsterdam, The Netherlands
[7] Magin, R.L., Fractional calculus in bioengineering, (2006), Begell House Publisher Connecticut
[8] Magin, R.L.; Abdullah, O.; Baleanu, D.; Zhou, X.H.J., Anomalous diffusion expressed through fractional order differential operators in the bloch – torrey equation, J. magn. reson., 190, 255-270, (2008)
[9] Nigmatullin, R.R., The statistics of the fractional moments: Is there any chance to “read quantitatively” any randomness?, Signal process., 86, 10, 2529-2547, (2006) · Zbl 1172.62303
[10] Oldham, K.B.; Spanier, J., The fractional calculus, (1974), Academic Press New York · Zbl 0428.26004
[11] Podlubny, I., Fractional differential equations, (1999), Academic Press · Zbl 0918.34010
[12] Kilbas, A.A.; Srivastava, H.H.; Trujillo, J.J., Theory and applications of fractional differential equations, (2006), Elsevier Amsterdam · Zbl 1092.45003
[13] Momani, S., A numerical scheme for the solution of multi-order fractional differential equations, Appl. math. comput., 182, 1, 761-770, (2006) · Zbl 1107.65119
[14] Ortigueira, M.D., On the initial conditions in continuous-time fractional linear systems, Signal process., 83, 11, 2301-2309, (2003) · Zbl 1145.94367
[15] Barbosa, R.S.; Machado, J.A.T.; Ferreira, I.M., Tuning of PID controllers based on bode’s ideal transfer function, Nonlinear dynam., 38, 1-4, 305-321, (2004) · Zbl 1134.93334
[16] Dinç, E.; Baleanu, D., Multicomponent quantitative resolution of binary mixtures by using continuous wavelet transform, J. AOAC int., 87, 2, 360-365, (2004)
[17] Dinç, E.; Baleanu, D., A new fractional wavelet approach for simultaneous determination of sodium and sulbactam sodium in a binary mixture, Spectrochim. acta, 63, 3, 631-638, (2006)
[18] Dinç, E.; Baleanu, D., Application of the wavelet method for the simultaneous quantitative determination of benazepril and hydrochlorothiazide in their mixtures, J. AOAC int., 87, 4, 834-841, (2004)
[19] Dinç, E.; Baleanu, D., A review on the wavelet transform applications in analytical chemistry, (), 265-285 · Zbl 1126.92064
[20] Dinç, E.; Baleanu, D.; Üstündağ, Ö., An approach to quantitative two-component analysis of a mixture containing hydrochlorothiazide and spironolactone in tablets by one-dimensional continuous Daubechies and biorthogonal wavelet analysis of UV-spectra, Spectros. lett., 36, 341-355, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.