A method and a system for generating a time-frequency representation of an aperiodic continuous input signal comprising generating a periodic train of short pulses having a repetition frequency, and sampling the signal temporally using the periodic train of short pulses to obtain a temporally sampled signal, the temporally sampled signal comprising a plurality of sampled copies of the input signal, each sampled copy being spaced in function of the repetition frequency of the periodic train of short pulses. The temporally sampled signal is delayed based on the repetition frequency to obtain a delayed temporally sampled signal comprising a plurality of delayed sampled copies, a spectral representation of a given delayed sampled copy being delayed in function of the repetition frequency. The delayed temporally sampled signal is evaluated over consecutive time slots to obtain, for each consecutive time slot, a respective output signal in the time-frequency domain.

In some implementations, a device may receive spectroscopic data associated with a dynamic process. The device may generate a principal component analysis (PCA) model based on a first block of spectra from the spectroscopic data. The device may project a second block of spectra from the spectroscopic data to the PCA model generated based on the first block of spectra. The device may determine a value of a metric associated with the second block based on projecting the second block of spectra to the PCA model. The device may determine whether the dynamic process has reached an end point based on the value of the metric associated with the second block.

A method and a system for generating a time-frequency representation of an aperiodic continuous input signal comprising generating a periodic train of short pulses having a repetition frequency, and sampling the signal temporally using the periodic train of short pulses to obtain a temporally sampled signal, the temporally sampled signal comprising a plurality of sampled copies of the input signal, each sampled copy being spaced in function of the repetition frequency of the periodic train of short pulses. The temporally sampled signal is delayed based on the repetition frequency to obtain a delayed temporally sampled signal comprising a plurality of delayed sampled copies, a spectral representation of a given delayed sampled copy being delayed in function of the repetition frequency. The delayed temporally sampled signal is evaluated over consecutive time slots to obtain, for each consecutive time slot, a respective output signal in the time-frequency domain.

In some implementations, a device may receive spectroscopic data associated with a dynamic process. The device may generate a principal component analysis (PCA) model based on a first block of spectra from the spectroscopic data. The device may project a second block of spectra from the spectroscopic data to the PCA model generated based on the first block of spectra. The device may determine a value of a metric associated with the second block based on projecting the second block of spectra to the PCA model. The device may determine whether the dynamic process has reached an end point based on the value of the metric associated with the second block.

In some implementations, a device may receive spectroscopic data associated with a dynamic process. The device may generate a principal component analysis (PCA) model based on a first block of spectra from the spectroscopic data. The device may project a second block of spectra from the spectroscopic data to the PCA model generated based on the first block of spectra. The device may determine a value of a metric associated with the second block based on projecting the second block of spectra to the PCA model. The device may determine whether the dynamic process has reached an end point based on the value of the metric associated with the second block.

In some implementations, a device may receive spectroscopic data associated with a dynamic process. The device may generate a principal component analysis (PCA) model based on a first block of spectra from the spectroscopic data. The device may project a second block of spectra from the spectroscopic data to the PCA model generated based on the first block of spectra. The device may determine a value of a metric associated with the second block based on projecting the second block of spectra to the PCA model. The device may determine whether the dynamic process has reached an end point based on the value of the metric associated with the second block.