DSP-based correction of spectrograms using cubic splines and Kalman filtering

Raw spectrograms are subject to systematic errors of an instrumental type that may be reduced provided a mathematical model of the instrumental imperfections is identified. It is assumed in the paper that this model has the form of an integral, convolution-type equation of the first kind whose kernel may be causal or not. The correction of the spectrograms consists in numerically solving this equation on the basis of the noisy data. Acquired by a spectrometer. An algorithm of correction is proposed which is based on the approximation of the solution with a spline function whose parameters are determined by means of a recursive Kalman-filter-based algorithm with a non-negativity constraint imposed on the set of feasible solutions. It is shown, using spectrophotometric data, that an improvement in the resolution of the spectrometer can be attained