We describe further potential of generalized 2D correlation analysis, aiming to realize the automation of the sequential order determination of signal variations. By modeling unimodal waveforms using quadratic functions, we can analytically express 2D correlation functions to yield an index to determine the sequential order. Based on the obtained results, we find an exception for determining the sequential order of signal variations. To resolve the exception, we suggest an extended way of interpreting the sequential order of signal intensity changes.
Keywords: Correlation; Hilbert transform; quadratic polynomial; sequential order; spectroscopy.