In-search-of-true-PAC

Discussing different methods of calculating Phase Amplitude Coupling

PAC Methods

CWT & MVL
Rid-rihaczek (old version, supposed to have implementation bug) & MVL
Rid-rihaczek (new version (neuroFreq), First tf-decomposition, then windowing) & MVL
Rid-rihaczek (old version, correctred versio) & MVL
Rid-rihaczek (new version (neuroFreq), First windowing, then tf-decomposition) & MVL
CWT & MI

Synthesizing the signal:
- The phase amplitude coupled signal has been generated following proposed method at the this article.
- Generating a signal composed of:
  - Random gaussian nosie of 1 second
  - coupled signal one:
    - Amplitude frequency: 40 Hz
    - Phase frequency: 5 Hz
  - coupled signal two:
    - Amplitude frequency: 60 Hz
    - Phase frequency: 9 Hz
  - coupled signal one + additive noise
  - coupled signal two + additive noise
PAC Comodulogram
- Generating comodulogram for each of the 5 sections of the signal
PAC dynamic
- Generating PAC dynamic through all of the 5 second signal
- Window length = 200 ms
- Window shift step = 100 ms
Statistical test
- Sample size: 100
- Population 1:
  - Coupled signals:
    - Random Phase freq in range: [4, 7]
    - Random Amp freq in range: [38, 42]
- Population 2:
  - Coupled signals:
    - Random Phase freq in range: [8, 11]
    - Random Amp freq in range: [55, 65]
- Null hypothesis:
  - PAC in range [4,8] and [35, 45] is higher for second population

Each of these methods has their own pros and cons
Rid-rihaczek can decompose frequency more precicely than the CWT. The CWT will skew the freuqency axes
MVL method is biased with amplitude signal and power (Note the comodulograms)
MI requires signals long enough (more than 500 samples)
MVL may detect fake couplings too but works preciecly well with actual couplings
MVL doesn't require permutations test but using it may lead to better results espcially when we use CWT
Curerntly MVL is much faster than MI