An equivalence between typical spectrographic data analysis and the formulations for time series analysis

We have demonstrated the equivalence of two formulations for data processing, which usually are studied separately and independently. Habitually, for time series analysis, like signals processed in communications, electronics, control sciences, etc., mathematical tools based on autocorrelations, cross-correlations or convolutions, etc., are applied. Another sort of formulations is applied for analysis in spectrographic techniques, where the data is usually processed with statistical procedures based on the least square method. The equivalence demonstrated between both methodologies opens new possibilities in time series analysis, in order to find predetermined structures in the acquired data. Also, all of the mathematical criteria often used in spectroscopic analysis (like the limit of detection, or the determination limit), could be applied in methods for analysis of data depending on time.