where , is the time shift of the input signal and is the time-dependant coefficients. We solve the under-determined linear system by using the shaping regularization method. The solution is the form below:

where is a vector of , the elements of vector is:

the elements of the matrix is:

where is the regularization parameter, is a shaping operator, and 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.

2020-07-18