RP-HPLC and UV Spectrophotometric Analysis of Paracetamol, Ibuprofen, and Caffeine in Solid Pharmaceutical Dosage Forms by Derivative, Fourier, and Wavelet Transforms: A Comparison Study

Table 1

Statistical analysis of the calibration graphs of the proposed spectrophotometric methods for PA (20–40 mg/L), IB (12–32 mg/L), and CA (1–3.5 mg/L) (n = 6).

Method divisor (mg/L)	Function	Compound	Wavelength (nm)	a	b	Sa	Sb	Sy·x	R^2
Derivative transform
Single divisor
CA 2	^1D	PA	225.2^1	3.2058	5.5814	0.0403	1.2421	0.6763	0.9994
PA 30	^1D	IB	212.8^1	0.1072	0.2296	0.0015	0.0357	0.0259	0.9992
PA 30	^1D	CA	270.7^1	0.3426	0.0074	0.0042	0.0102	0.0088	0.9994
Double divisor
IB 20 + CA 2	^1D	PA	238.8^1	5.2637	38.076	0.0535	1.6502	0.8985	0.9996
PA 30 + CA 2	^1D	IB	236.0^1	−0.0535	0.0019	0.0006	0.0130	0.0095	0.9996
PA 30 + IB 20	^1D	CA	262.0^1	0.2512	−0.0319	0.0052	0.0126	0.0110	0.9983
Successive divisor
CA 2; IB 20/CA 2	^1D	PA	279.8^1	1.4573	2.6761	0.0302	0.9307	0.5067	0.9983
CA 2; PA 32.5/CA 2	^1D	IB	243.2^1	0.0068	−0.0206	0.0002	0.0045	0.0032	0.9968
PA 32.5; IB 20/PA 32.5	^1D	CA	285.6^1	−0.6723	0.1036	0.0076	0.0183	0.0159	0.9995
Fourier transform
Double divisor
IB 20 + CA 2	cosxi + cos (xi + 60°)	PA	235.0	0.8681	−1.8316	0.0183	0.0620	0.0106	0.9977
	cos2xi + cos2 (xi + 60°)	PA	245.0	−0.1417	0.2900	0.0026	0.0090	0.0015	0.9982
	sinxi – sin (xi + 60°)	PA	235.0	−0.5012	1.0574	0.0105	0.0358	0.0061	0.9977
	sin2xi – sin2(xi + 60°)	PA	245.0	0.2454	−0.5024	0.0046	0.0156	0.0026	0.9982
	cosxi + cos(xi + 45°)	PA	245.0^1	−2.2482	4.4903	0.0460	0.1556	0.0266	0.9979
	cos2xi + cos2(xi + 45°)	PA	245.0	−0.3837	0.7838	0.0061	0.0207	0.0035	0.9987
	sinxi – sin (xi + 45°)	PA	245.0	0.9312	−1.8599	0.0190	0.0644	0.0110	0.9979
	sin2xi – sin 2(xi + 45°)	PA	237.0	−0.5673	1.1944	0.0132	0.0448	0.0076	0.9972
Wavelet transform
Single divisor
CA 2	sym6	PA	215.8	−2.7258	−21.640	0.5012	1.5803	0.8604	0.9986
	haar	PA	224.8	−5.0086	−16.222	0.0954	2.9443	1.6030	0.9986
	coif	PA	216.6	−2.5529	−18.769	0.0407	1.2567	0.6842	0.9990
	mexh	PA	251.3^1	15.051	74.527	0.1359	4.1929	2.2828	0.9997
IB 20	sym6	PA	247.6	9.4930	80.257	0.2992	9.2315	5.0261	0.9960
	haar	PA	258.5	9.2566	70.689	0.1533	4.7315	2.5761	0.9989
	coif3	PA	226.0	−5.6236	−47.161	0.1208	3.7285	2.0300	0.9982
PA 32	sym6	IB	219.5	0.1235	−0.0457	0.010	0.0221	0.0161	0.9998
	sym6	CA	227.6^1	−0.1774	−0.0040	0.0022	0.0052	0.0045	0.9994
	haar	IB	209.3	−0.1016	0.7232	0.0016	0.0371	0.0269	0.9990
	haar	CA	269.0	0.3011	0.0134	0.0046	0.0110	0.0096	0.9991
	coif3	IB	220.3	0.1259	−0.0264	0.0011	0.0243	0.0176	0.9997
	coif3	CA	228.6	−0.1704	−0.0075	0.0018	0.0044	0.0038	0.9995
	mexh	IB	225.3^1	0.2874	0.847	0.0041	0.0950	0.069	0.9992
Double divisor
PA 30 + CA 2	sym6	IB	235.9	−0.1158	−0.5166	0.0027	0.0612	0.0444	0.9979
	haar	IB	229.8	0.1606	0.2217	0.0032	0.0744	0.0540	0.9984
	coif3	IB	218.5	0.1617	−1.1876	0.0020	0.0461	0.0335	0.9994
	mexh	IB	220.1^1	0.2733	9.3074	0.0039	0.0890	0.0646	0.9992
IB 20 + CA 2	sym6	PA	298.5	2.4206	8.2337	0.0680	2.0925	1.1380	0.9969
	haar	PA	256.8	3.9248	32.492	0.0558	1.7155	0.9330	0.9992
	coif3	PA	299.8	2.5651	8.8463	0.0741	2.2860	1.2446	0.9967
	mexh	PA	248.6^1	6.6815	54.282	0.0947	2.9212	1.5905	0.9992
Successive divisor
PA 32.5; IB 20/PA 32.5	haar	CA	263.7^1,2	238.98	−64.253	3.0612	7.3671	6.4030	0.9993
	coif3	CA	278.8	38.057	3.3329	0.2544	0.6122	0.5321	0.9998
CA 2; PA 32.5/CA 2	sym6	IB	216.8	0.2388	−1.2639	0.0011	0.0243	0.0177	0.9999
	haar	IB	216.6	0.6190	−0.2462	0.0023	0.0538	0.0391	0.9999
	coif3	IB	210.4	0.2345	3.6966	0.0028	0.0649	0.0471	0.9994
PA 32.5; CA 2/PA 32.5	sym6	IB	220.5^1,2	−29.814	104.61	0.3792	8.7352	6.3452	0.9994
	coif3	IB	242.0	14.208	78.234	0.0638	1.4704	1.0681	0.9999
CA 2; IB 20/CA 2	sym6	PA	251.1	33.526	299.80	0.4087	12.609	6.8653	0.9994
	haar	PA	249.3	−16.153	−140.13	0.1689	5.2124	0.8379	0.9996
	mexh	PA	243.2	10.856	29.469	0.1183	3.6505	1.9875	0.9995
IB 20; CA 2/IB 20	sym6	PA	212.0^1,2	−165.44	−1490.1	2.5918	79.969	43.539	0.9990
	haar	PA	225.3	−47.847	−313.61	0.3201	9.8771	5.3776	0.9998
	coif3	PA	247.9	9.9188	81.622	0.0758	2.3398	1.2739	0.9998
	mexh	PA	248.6	−10.751	−154.96	0.0988	3.0491	1.6601	0.9997

Y = a × C + b, where C is the concentration in mg/L and Y is in signal’s amplitude units; a: slope; b: intercept; S_a: standard error of the slope; S_b: standard error of the intercept; S_y.x: standard error of the regression; R²: coefficient of determination. Y = a × lnC + b. ¹Wavelengths used for assay (the highest absolute values of the slopes of the developed spectrophotometric methods using the same type of divisor for each compound). ²Wavelengths used for the dissolution test (the highest absolute values of the slopes of all the developed spectrophotometric methods for each compound).