Equation 27 can be written as a matrix form:
is the time shift
of the input signal
is the time-dependant coefficients.
We solve the under-determined linear system by using the shaping regularization method.
The solution is the form below:
is a vector of
, the elements of vector
the elements of the matrix
where is the regularization parameter,
is a shaping operator,
stands for the complex conjugate of
We can use the conjugate gradient method to find the solution of the linear system.
The NPM (Fomel, 2013) can be summarized as follows:
After we decompose the input signal into narrow-band components,
we compute the time-frequency distribution of the input signal
using the Hilbert transform of the intrinsic mode functions.