pysdkit.lmd#

Created on 2025/01/31 21:35:05 @author: Whenxuan Wang @email: wwhenxuan@gmail.com

pysdkit._lmd.lmd

Created on 2025/01/31 21:35:18 @author: Whenxuan Wang @email: wwhenxuan@gmail.com

pysdkit._lmd.rlmd

Created on 2025/01/31 23:33:43 @author: Whenxuan Wang @coauthor: Wentong Zhao @email: wwhenxuan@gmail.com

lmd.lmd#

Created on 2025/01/31 21:35:18 @author: Whenxuan Wang @email: wwhenxuan@gmail.com

class pysdkit._lmd.lmd.LMD(K: int = 5, endpoints: bool = True, max_smooth_iter: int = 15, max_envelope_iter: int = 200, envelope_epsilon: float = 0.01, convergence_epsilon: float = 0.01, min_extrema: int = 5)[source]#

Bases: object

Local Mean Decomposition

Jia, Linshan, et al. “The Empirical Optimal Envelope and Its Application to Local Mean Decomposition.” Digital Signal Processing, vol. 87, Elsevier BV, Apr. 2019, pp. 166–77, doi:10.1016/j.dsp.2019.01.024.

Python code: shownlin/PyLMD

MATLAB code: https://www.mathworks.com/matlabcentral/fileexchange/107829-local-mean-decomposition?s_tid=srchtitle

__call__(signal: ndarray, K: int | None = None) → ndarray[source]#

allow instances to be called like functions

__init__(K: int = 5, endpoints: bool = True, max_smooth_iter: int = 15, max_envelope_iter: int = 200, envelope_epsilon: float = 0.01, convergence_epsilon: float = 0.01, min_extrema: int = 5) → None[source]#
Parameters:

  • K – the maximum number of IFMs to be decomposed

  • endpoints – whether to treat the endpoint of the signal as a pseudo-extreme point

  • max_smooth_iter – maximum number of iterations of moving average algorithm

  • max_envelope_iter – maximum number of iterations when separating local envelope signals

  • envelope_epsilon – terminate processing when obtaining pure FM signal

  • convergence_epsilon – terminate processing when modulation signal converges

  • min_extrema – minimum number of local extrema

__module__ = 'pysdkit._lmd.lmd'#
__str__() → str[source]#

Get the full name and abbreviation of the algorithm

__weakref__#

list of weak references to the object (if defined)

extract_product_function(signal: ndarray) → ndarray[source]#

Perform one time local mean decomposition algorithm

find_extrema(signal: ndarray) → ndarray[source]#

Find all local extreme points of the signal

fit_transform(signal: ndarray, K: int | None = None) → ndarray[source]#

Signal decomposition using Local Mean Decomposition (LMD) algorithm

Parameters:

  • signal – the time domain signal (1D numpy array) to be decomposed

  • K – the maximum number of IFMs to be decomposed

Returns:

IMFs

is_monotonous(signal: ndarray) → bool[source]#

Determine whether the signal is a (non-strict) monotone sequence

static is_monotonous_decrease(signal: ndarray) → bool[source]#

Determine whether the input signal is monotonically decreasing

static is_monotonous_increase(signal: ndarray) → bool[source]#

Determine whether the input signal is monotonically increasing

static is_smooth(signal: ndarray, n: int) → bool[source]#

Determine whether a signal is smooth

local_mean_and_envelope(signal: ndarray, extrema)[source]#

Calculate the local mean function and local envelope function according to the location of the extreme points

moving_average_smooth(signal: ndarray, window: int) → ndarray[source]#

Smooth the input signal by sliding average

lmd.rlmd#

Created on 2025/01/31 23:33:43 @author: Whenxuan Wang @coauthor: Wentong Zhao @email: wwhenxuan@gmail.com

class pysdkit._lmd.rlmd.RLMD(max_imfs: int | None = 10, max_iter: int | None = 30, smooth_mode: str | None = 'ma', ma_span: str | None = 'liu', ma_iter_mode: str | None = 'fixed', stop_threshold: Tuple[float, float, float] | None = (0.005, 0.7, 0.005), extd_r: float | None = 0.2, sifting_stopping_mode: str | None = 'liu', min_peak: int | None = 3, min_ratio: float | None = 0.001)[source]#

Bases: object

Robust Local Mean Decomposition

The RLMD is an improved local mean decomposition powered by a set of optimization strategies. The optimization strategies can deal with boundary condition, envelope estimation, and sifting stopping criterion in the LMD. It simultaneously extracts a set of mono-component signals (called product functions) and their associated demodulation signals (i.e. AM signal and FM signal) from a mixed signal, which is the most attracting feature comparing with other adaptive signal processing methods, such as the EMD. The RLMD can be used for time-frequency analysis.

Zhiliang Liu, Yaqiang Jin, Ming J. Zuo, and Zhipeng Feng. Time-frequency representation based on robust local mean decomposition for multi-component AM-FM signal analysis. Mechanical Systems and Signal Processing. 95: 468-487, 2017. Liu Zhiliang (2025). Robust Local Mean Decomposition (RLMD) (https://www.mathworks.com/matlabcentral/fileexchange/66935-robust-local-mean-decomposition-rlmd), MATLAB Central File Exchange. Retrieved July 13, 2025.

__call__(signal: ndarray, return_all: bool | None = False) → ndarray[source]#

Allow instances to be called like functions

__init__(max_imfs: int | None = 10, max_iter: int | None = 30, smooth_mode: str | None = 'ma', ma_span: str | None = 'liu', ma_iter_mode: str | None = 'fixed', stop_threshold: Tuple[float, float, float] | None = (0.005, 0.7, 0.005), extd_r: float | None = 0.2, sifting_stopping_mode: str | None = 'liu', min_peak: int | None = 3, min_ratio: float | None = 0.001)[source]#

The above parameters are the default parameters of the algorithm. Please modify and adjust them according to the specific data when using them.

Parameters:

  • max_imfs – Maximum number of intrinsic mode functions to be decomposed.

  • max_iter – max iteration number in a PF sifting process.

  • smooth_mode – ma - moving average, spline - pchip.

  • ma_span – pdmax span method, see function ma_span.

  • ma_iter_mode – fixed or dynamic span for iterate ma.

  • stop_threshold – sifting stopping thresholds for Rilling’s criterion.

  • extd_r – end extension length to original data.

  • sifting_stopping_mode – the sifting stoppling optimizaion.

  • min_peak – When the number of remaining extreme points of the input signal is less than a certain value, the algorithm stops iterating.

  • min_ratio – When the energy of the remaining signal is less than a certain value, the algorithm stops iterative updating.

__module__ = 'pysdkit._lmd.rlmd'#
__str__() → str[source]#

Get the full name and abbreviation of the algorithm

__weakref__#

list of weak references to the object (if defined)

_get_best_span(ind_extr: ndarray, x: ndarray) → Tuple[ndarray | int, int][source]#

Moving average span selection. Return the best span of moving average

Parameters:

  • ind_extr – indices of extremum of x

  • x – the input signal to be decomposed.

Returns:

  • span : int, Optimal moving-average span (always odd).

  • smax : int, Maximum step between consecutive extrema.

_initial_inputs(signal: ndarray) → Tuple[ndarray | float, ndarray, ndarray, ndarray, ndarray, ndarray][source]#
_is_sifting_stopping(a_j: ndarray, j: ndarray, fv_i: ndarray) → Tuple[bool, ndarray][source]#

Sifting stopping criterion of Robust Local Mean Decomposition.

_itrma(x: ndarray, span: int, smax: int) → ndarray[source]#

Iterative moving average dynamic step.

Parameters:

  • x – the input signal to be decomposed.

  • span – int, moving-average span (always odd).

  • smax – Maximum step between consecutive extrema.

Returns:

get the iterative moving average of the input signal.

_lmd_mean_amp(x: ndarray) → Tuple[ndarray, ndarray, ndarray | int][source]#

Compute mean function and amplitude function of x in LMD

Parameters:

x – the input signal.

Returns:

the results of mean iterative moving average

_stop_lmd(signal: ndarray, signal_energy: ndarray | float) → bool[source]#

Stopping criterion of LMD algorithm. Check if there are enough (3) extrema to continue the decomposition

Parameters:

  • signal – The original input signal or the residual component of the signal

  • signal_energy – The energy of the original signal

Returns:

fit_transform(signal: ndarray, return_all: bool | None = False) → ndarray | Tuple[ndarray, ndarray, ndarray][source]#

This funcion perform the local mean decompose (LMD) on the input signal, and return the product function (pfs), and their corresponding instantaneous amplititde(ams) and frequency modulation signal(fms).

Parameters:

  • signal – 1D ndarray input signal to be decomposed.

  • return_all – whether to return all information in the decomposition loop.

Returns:

the decomposition result of the input 1D ndarray signal by Local Mean Decomposition.