Method and System of Signal Processing for Phase-Amplitude Coupling and Amplitude-Amplitude coupling

A method of signal processing for amplitude-amplitude coupling, the method comprising:

• step 1. receiving a non-stationary signal with amplitude and frequency changes over time;
• step 2. decomposing the non-stationary signal by an ensemble empirical mode decomposition (EEMD) into a plurality of intrinsic mode functions (IMFs), wherein each of the IMFs is an expression of one banded frequency component in the non-stationary signal, and each banded frequency component corresponds to one of the IMFs;
• step 3. decomposing a first IMF with a region of interest by the EEMD into a plurality of envelop functions, wherein each envelop function is an expression of one envelope frequency in the first IMF, and each envelope frequency corresponds to one of the envelop functions;
• step 4. selecting a first envelop function from the envelop functions, retrieving a phase function of the first envelop function, and obtaining a plurality of first-IMF envelope cycle frequencies, wherein each first-IMF envelope cycle frequency corresponds to the variation between cycles of the first IMF;
• step 5. selecting a second IMF from the IMFs at the frequency higher than the first IMF, retrieving an amplitude function of the second IMFs, and obtaining a plurality of second-IMF cycle frequencies, wherein each second-IMF cycle frequency corresponds to the variation of the second IMF;
• and
• step 6. comparing the phase function with the amplitude function on a time domain to generate a scattering plot, wherein the scattering plot is based on the first-IMF envelope cycle frequencies corresponding to the second-IMF cycle frequencies.
• step 7. repeating step 5 to step 6, until generate the scattering plots by comparing the phase function of the first envelop function with the amplitude function of each another IMF at the frequency higher than the first IMF.

A system of signal processing for phase-amplitude coupling:

• a signal collecting unit, receiving a non-stationary signal with amplitude and frequency changes over time;
• a signal processing unit, connected to the signal collecting unit, decomposing the non-stationary signal by an ensemble empirical mode decomposition (EEMD) into a plurality of intrinsic mode functions (IMFs), wherein each of the IMFs is an expression of one banded frequency component in the non-stationary signal, and each banded frequency component corresponds to one of the IMFs;
• a phase function processing unit, connected to the signal processing unit, selecting a first IMF with a region of interest, retrieving a phase function of the first IMF, and obtaining a plurality of first-IMF cycle frequencies, wherein each first-IMF cycle frequency corresponds to the increment of the phase function across the cycle;
• an amplitude function processing unit, connected to the phase function processing unit, selecting a second IMF, retrieving an amplitude function of the second IMFs, and obtaining a plurality of second-IMF cycle frequencies according to the variation between of the second IMF;
• and
• a signal comparison unit, connected to the amplitude function processing unit, comparing the phase function with the amplitude function on a time domain, generating a scattering plot according to the first-IMF cycle frequencies corresponding to the second-IMF cycle frequencies;
• Wherein the system repeats signal processing from the amplitude function processing unit to signal comparison unit until generate the scattering plots by comparing the phase function of the first IMF with the amplitude function of each another IMF.

A system of signal processing for amplitude-amplitude coupling:

• a signal collecting unit, receiving a non-stationary signal with amplitude and frequency changes over time;
• a signal processing unit, connected to the signal collecting unit, comprising a first mode and a second mode, the first mode decomposes the non-stationary signal by an ensemble empirical mode decomposition (EEMD) into a plurality of intrinsic mode functions (IMFs), wherein each of the IMFs is an expression of one banded frequency component in the non-stationary signal, and each banded frequency component corresponds to one of the IMFs;
• then the second mode decomposes a first IMF with a region of interest by the EEMD into a plurality of envelop functions, wherein each of the envelop functions is an expression of one envelope frequency in the first IMF, and each envelope frequency corresponds to one of the envelop functions;
• a phase function processing unit, connected to the signal processing unit, selecting a first envelop function from the envelop functions, retrieving a phase function of the first envelop function, obtaining a plurality of first-IMF envelope cycle frequencies, wherein each first-IMF envelope cycle frequency corresponds to the variation between cycles of the first IMF;
• an amplitude function processing unit, connected to the phase function processing unit, selecting a second IMF from the IMFs at the frequency higher than the first IMF, retrieving an amplitude function of the second IMFs, and obtaining a plurality of second-IMF cycle frequencies, wherein each second-IMF cycle frequency corresponds to the variation of the second IMF;
• and
• a signal comparison unit, connected to the signal processing unit, comparing the phase function with the amplitude function on a time domain to generate a scattering plot, wherein the scattering plot is based on the first-IMF envelope cycle frequencies corresponding to the second-IMF cycle frequencies.
• Wherein the system repeats signal processing from the amplitude function processing unit to the signal comparison unit until generate the scattering plots by comparing the phase function of the first envelop function with the amplitude function of each another IMF at the frequency higher than the first IMF.