Solution 3.1 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

1. The following graph is obtained.

Notice how there appear to be two peaks, which is most evident from the asymmetry.

 

2. The results of the five methods for smoothing are given below.

(a)	(b)	(c)	(d)	(e)
0.0256		0.0184
0.0270	0.0332	0.0123	0.0180
0.0313	0.0474	0.0255	0.0186	-0.0264
0.0548	0.1455	0.0428	-0.0097	0.0239
0.2018	0.2591	0.0196	0.1029	0.1401
0.3521	0.4071	0.2699	0.2880	0.3375
0.5567	0.5401	0.5777	0.5747	0.5819
0.7353	0.6441	0.9067	0.8532	0.7832
0.8624	0.7440	0.9860	0.9824	0.9295
0.8692	0.8073	0.9546	0.9389	0.9427
0.8224	0.7961	0.8288	0.8420	0.8288
0.7465	0.7850	0.6878	0.7013	0.7705
0.6949	0.7093	0.6423	0.6678	0.7130
0.6479	0.5878	0.6503	0.6888	0.6407
0.5166	0.4984	0.6952	0.5883	0.5550
0.4298	0.3972	0.4708	0.4652	0.4418
0.3107	0.2978	0.2127	0.2867	0.3121
0.1403	0.1772	0.0954	0.1007	0.1109
0.0016	0.0797	0.0358	-0.0391	-0.0275
-0.0164	0.0100	-0.1158	-0.0672	-0.0650
-0.0358	-0.0160	-0.1298	-0.0804
-0.0619		-0.0179

 

The graphs are as follows.

3.  The MA filters (a) and (b) blur out the peaks, this is because they fit a linear model and so result in lost resolution. The 5-point MA filter preserves a small amount of resolution. The 5- and 7-point SG filters preserve resolution with the 7-point filter reducing noise more. The 9-point filter loses resolution. A 7-point quadratic SG filter seems optimal for this dataset.