Smoothing algorithm 360 Subject

Deconvolution Algorithms. The correlation function for broad distributions is a sum of single exponentials. This ill-conditioned mathematical problem is not subject to the usual criteria for goodness-of-fit. Size resolution is ultimately limited by the noise on the measured correlation function, and measurements for several hours (13) are required to obtain accurate widths. Peaks closer than about 2 1 are unlikely to be resolved unless a-priori assumptions are invoked to constrain the possible solutions. Such constraints should be stated explicitly otherwise, the results are misleading. Constraints that work well with one type of distribution and one set of data often fail with others. Thus, artifacts including nonexistent bi-, tri-, and quadramodals abound. Many particle size distributions are inherently nonsmooth, and attempts to smooth the data prior to deconvolution have not been particularly successful. 

To summarize TDS data and get a descriptive picture of each product, the most common representation is the TDS curve. The procedure (Section 13.4.2) considers each attribute separately. For each point of time, the proportion of evaluations (subject X replication) for which the given atUibute was assessed as dominant is computed. These proportions are smoothed over time (e.g. using moving average or a more sophisticated algorithm such as SAS/TRANSREG) and displayed as curves of the evolution of the dominance rate for each attribute. In the example of Fig. 13.2, the... 

Processing the previously acquired data by subjection to a mathematical treatment such as curve smoothing (e.g. with the Savitzky—Golay algorithm), derivation, calibration or spectral refining. Data can be also exported to be processed with other software (e.g. Excel spreadsheet). 

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