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The selection of the optimal mother wavelet is the most important step in the CWT method. It may be that two or more CWT methods give satisfactory results, so the most suitable CWT method has to be found for the problem. Various wavelet families with different scales were tested to find the optimal signal processing for obtaining desirable calibration graphs and reliable determination of investigated metal ions. Biorthogonal (bior2.4) (a = 160), Biorthogonal (bior3.9) (a = 160) and coiflet (coif3) (a = 100) were selected as optimal conditions, because they gave the highest sensitivity with large slope values in the linear regression equations for the two subjected compounds. Absorption spectra of standard solutions of aluminum and bismuth with different concentrations were recorded in the spectral region 400–650 nm against a blank solution. The absorption spectra were transferred from Excel to the wavelet domain in a MATLAB environment. The absorption spectra of the standard solutions of aluminum and bismuth were transferred into the wavelet domain by bior2.4, bior3.9 and coif3, and CWT spectra were obtained by plotting Ca,b coefficients versus wavelengths, as can be seen in Figure 2. The zero cross-points were used for simultaneous determination of the metal ions, and the calibration graphs of each ion were obtained. The calibration graphs of aluminum for the wavelet methods were created by plotting the transformed signals versus the concentration of bismuth at the zero-crossing points, and contrariwise. The calibration graphs of bior2.4 were obtained by measuring the transformed signals at 477 and 576 nm for aluminum (corresponding to the zero crossing point of bismuth) and at 442 and 555 nm for bismuth (corresponding to the zero crossing point of aluminum). By using a similar method, the calibration graphs for bior3.9 and coif3 were created by measuring the signal domain at 435, 529, 622, 495 and 566 nm for aluminum and at 500, 400, 605, 452 and 540 nm for bismuth. Linear regression analysis and the statistical results are summarized in Table 1.
Table 1

Statistical results of calibration graphs obtained by the CWT method

Mother waveletλ (nm)Linear range (μg mL−1)Regression equationR2aLODb
Bior 2.4 477 0.10–11.00 A = 0.1783CAl + 0.4668 0.9739 0.0072 
Bior 2.4 576 0.10–11.00 A = −0.0755CAl − 0.2527 0.9739 0.0172 
Bior 2.4 442 0.10–7.00 A = −0.2261CBi − 0.1593 0.9993 0.0064 
Bior 2.4 555 0.10–7.00 A = 0.2860CBi + 0.2425 0.9978 0.0051 
Bior 3.9 435 0.10–11.00 A = −0.1934CAl − 0.4515 0.9736 0.0067 
Bior 3.9 529 0.10–11.00 A = 0.1833CAl + 0.4986 0.9740 0.0070 
Bior 3.9 622 0.10–11.00 A = −0.0700CAl − 0.2292 0.9732 0.0185 
Bior 3.9 500 0.10–7.00 A = −0.4043CBi − 0.3156 0.9986 0.0036 
Bior 3.9 400 0.10–7.00 A = 0.2191CBi + 0.1572 0.9992 0.0066 
Bior 3.9 605 0.10–7.00 A = 0.2401CBi + 0.2161 0.9970 0.0061 
Coif 3 495 0.10–11.00 A = 0.0988CAl + 0.2536 0.9748 0.0131 
Coif 3 566 0.10–11.00 A = −0.0564CAl − 0.1740 0.9742 0.0230 
Coif 3 452 0.10–7.00 A = −0.1211CBi − 0.0688 0.9997 0.0120 
Coif 3 540 0.10–7.00 A = 0.2566CBi + 0.2163 0.9979 0.0057 
Mother waveletλ (nm)Linear range (μg mL−1)Regression equationR2aLODb
Bior 2.4 477 0.10–11.00 A = 0.1783CAl + 0.4668 0.9739 0.0072 
Bior 2.4 576 0.10–11.00 A = −0.0755CAl − 0.2527 0.9739 0.0172 
Bior 2.4 442 0.10–7.00 A = −0.2261CBi − 0.1593 0.9993 0.0064 
Bior 2.4 555 0.10–7.00 A = 0.2860CBi + 0.2425 0.9978 0.0051 
Bior 3.9 435 0.10–11.00 A = −0.1934CAl − 0.4515 0.9736 0.0067 
Bior 3.9 529 0.10–11.00 A = 0.1833CAl + 0.4986 0.9740 0.0070 
Bior 3.9 622 0.10–11.00 A = −0.0700CAl − 0.2292 0.9732 0.0185 
Bior 3.9 500 0.10–7.00 A = −0.4043CBi − 0.3156 0.9986 0.0036 
Bior 3.9 400 0.10–7.00 A = 0.2191CBi + 0.1572 0.9992 0.0066 
Bior 3.9 605 0.10–7.00 A = 0.2401CBi + 0.2161 0.9970 0.0061 
Coif 3 495 0.10–11.00 A = 0.0988CAl + 0.2536 0.9748 0.0131 
Coif 3 566 0.10–11.00 A = −0.0564CAl − 0.1740 0.9742 0.0230 
Coif 3 452 0.10–7.00 A = −0.1211CBi − 0.0688 0.9997 0.0120 
Coif 3 540 0.10–7.00 A = 0.2566CBi + 0.2163 0.9979 0.0057 

aCorrelation coefficient.

bLimit of detection.

Figure 2

CWT spectra of aluminum (a1) 0.1 μg mL−1, (b1) 3.0 μg mL−1, (c1) 5.0 μg mL−1, (d1) 7.0 μg mL−1, (e1) 9.0 μg mL−1, (f1) 11.0 μg mL−1 and bismuth (a2) 0.1 μg mL−1, (b2) 1.0 μg mL−1, (c2) 2.5 μg mL−1, (d2) 4.0 μg mL−1, (e5) 5.5 μg mL−1, (f2) 7.0 μg mL−1 by (a) bior2.4 (b) bior3.9 and (c) coif3.

Figure 2

CWT spectra of aluminum (a1) 0.1 μg mL−1, (b1) 3.0 μg mL−1, (c1) 5.0 μg mL−1, (d1) 7.0 μg mL−1, (e1) 9.0 μg mL−1, (f1) 11.0 μg mL−1 and bismuth (a2) 0.1 μg mL−1, (b2) 1.0 μg mL−1, (c2) 2.5 μg mL−1, (d2) 4.0 μg mL−1, (e5) 5.5 μg mL−1, (f2) 7.0 μg mL−1 by (a) bior2.4 (b) bior3.9 and (c) coif3.

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