Two-dimensional convolute integers for analytical instrumentation

Abstract

As new analytical instruments and techniques emerge with increased dimensionality, a corresponding need is seen for data processing logic which can appropriately address the data. Two-dimensional measurements reveal enhanced unknown mixture analysis capability as a result of the greater spectral information content over two one-dimensional methods taken separately. It is noted that two-dimensional convolute integers are merely an extension of the work by Savitzky and Golay (1964). It is shown that these low-pass, high-pass and band-pass digital filters are truly two-dimensional and that they can be applied in a manner identical with their one-dimensional counterpart, that is, a weighted nearest-neighbor, moving average with zero phase shifting, convoluted integer (universal number) weighting coefficients.