Correlogram

One could consider the correlogram to be a snapshot of past events. We must memorize the detector signals and valve positions over a period of time and then calculate a correlogram with this data. To obtain a more up-to-date snapshot we must return to the array of data and calculate another correlogram based on the newest information which has been placed in the array. 

Figure 5. Construction of correlograms. a Detector signal generated by the sample injected over a period of time according to the PRBS shown below b. Calculation of correlation coefficients, c. Correlogram.

Correlation of the code with itself (autocorrelation) yields only one correlation point in the time domain defined by the sequence and the unit code interval (see Figure 5c) and an otherwise clean baseline. Since the detector in our chromatogram just follows what the sample valve is doing, it also should be a pseudo random sequence and the cross-correlation of input and output is really an autocorrelation and thus yields the single pulse correlogram with an otherwise clean baseline. 

Multiple Peaks. Finally, we must answer the question of how this method yields chromatograms containing many peaks and whether the correlogram intensity is related to component concentration ... 

Its special properties offer the possibility of reducing the so-called correlation noise, caused by a limited correlation time. CC is essentially statistical by nature. The system noise (detector noise) is not correlated with the input PRBS the noise in the correlogram, resulting from the detector noise, is converging to zero with increasing correlation time. 

Figure 5 represents a correlogram of this analysis obtained with the correlator and a modified HPLC system. The concentration of each component is only 0.2 ppm, an enhancement of 30. In Figure 6 the response trace leading to the correlogram of Figure 5 is shown. 

Figure 7 shows an enlarged part of a complex correlogram, displayed after correlation by the correlator. The area of one of the peaks is shown. 

Figure 5. Correlogram corresponding to Figure 4 with slightly different separation conditions. The concentration of each component is 0.2 ppm.

Figure 6. Detector output during correlation leading to the correlogram of Figure 5.

Figure 7. Enlarged part of a correlogram displayed on a TV-screen.

More research has to be done. One area is the influence of non-linearity which causes an extra baseline noise in the correlogram. Injection systems for other kinds of chromatography, in particular GC, have to be developed. The ability to detect very small differences between the solute concentrations in the background and the sample has to be investigated. 

Fig. 11. Correlogram of a phenol sample. Detection limit is approximately 3 ppt (3.10 g r ).

Re archers are active in the field of correlation gaschromatography and correlation HPLC " the first application in trace analysis was introduced in 1970 A typical example of the noise reduction property is the determination of a calibration graph of phenol for the higher concentrations with conventional chromatography, and extended to very low concentrations by CC (Fig. 10). The detection limit achieved is about 3 ppt (Laeven et al. ). A correlogram of 10 ng/1 phenol mple is shown in... 

The coefficient of correlation ranges from 1 to —1, denoting, respectively, perfect positive (both points in each couple have the same concentration) and perfect negative (one point is pure minor, the other is pure major) correlations. Figure 7.37 gives some typical correlograms. 

Fig. 7.37 Typical correlograms. (a) Along a line perpendicular to an equally spaced striped texture, (b) Over an area of a checkered board texture, (c) Along a line of an extruded film, as shown in Fig. 7.34, perpendicular to the extrusion direction.

Spatial autocorrelation and correlograms were used to describe the microscale spatial patterns of chlorophyll a concentration and seawater excess... 

In addition to obtaining correlograms, a large battery of methods are available to smooth time series, many based on so-called windows , whereby data are smoothed over a number of points in time. A simple method is to take the average reading over five points in time, but sometimes this could miss out important information about cyclicity especially for a process that is sampled slowly compared to the rate of oscillation. A number of linear filters have been developed which are apphcable to this time of data (Section 3.3), this procedure often being described as convolution. 

The most basic calculation is that of an auto-correlogram. Consider die information depicted in Figure 3.13, which represents a process changing with time. It appears that there is some cyclicity but this is buried within the noise. The data are presented in... 

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