InstantFrequencyOCM​ethod

Instantaneous frequency routine which is robust in case of non-zero mean and linearly shifted data.

Instantaneous frequency is computed from the Analytic Signal by Osculating Circle method.
The Instantaneous Phase is derived from the particle velocity series rather than
directly from the particle trajectory series - the latter is used by the traditional
Gabor's method. This lets to more reliable Instantaneous Frequency estimation.
This method overcomes the problem of non-physical negative Instantaneous
Frequencies which usually occurs if the Gabor's method is applied to
non-zero mean or linearly shifted data.
The algorithm is based on Osculating circle method described in:

Hsu, Ming-Kuang, Jiun-Chyuan Sheu, and Cesar Hsue.
"Overcoming the Negative Frequencies-Instantaneous Frequency and
Amplitude Estimation Using Osculating Circle Method."
Journal of Marine Science and Technology 19.5 (2011): 514-521.

The three point formula is used for numerical derivation of the
particle trajectory and instantaneous phase.

input : input signal as column-wise matrix
sample rate [ Hz ]
output: instantaneous frequency [ Hz ] as column-wise matrix