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‎README.md‎

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@@ -107,7 +107,6 @@ plot_IMFs(signal, IMFs) # per-channel panels
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| [`BMEMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_emd2d/bmemd.py) (Bidimensional Multivariate Empirical Mode Decomposition) | [[paper]](https://ieeexplore.ieee.org/document/8805082) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/72343-bidimensional-multivariate-empirical-mode-decomposition?s_tid=FX_rc1_behav) | ✔️ |
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| [`CEEMDAN`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_emd/ceemdan.py) (Complete Ensemble EMD with Adaptive Noise) | [[paper]](https://ieeexplore.ieee.org/document/5947265) | [[code]](https://github.com/laszukdawid/PyEMD/blob/master/PyEMD/EEMD.py) | ✔️ |
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| [`TVF_EMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_emd/tvf_emd.py) (Time Varying Filter Based EMD) | [[paper]](https://www.sciencedirect.com/science/article/pii/S0165168417301135) | [[code]](https://github.com/stfbnc/pytvfemd/tree/master) | ✔️ |
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| [`EFD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_emd/efd.py) (Empirical Fourier Decomposition) | [[paper]](https://www.sciencedirect.com/science/article/abs/pii/S0888327021005355) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/97747-empirical-fourier-decomposition-efd) | ✔️ |
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| [`FAEMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_faemd/faemd.py) (Fast and Adaptive EMD) | [[paper]](https://ieeexplore.ieee.org/document/8447300) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/71270-fast-and-adaptive-multivariate-and-multidimensional-emd) | ✔️ |
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| [`FAEMD2D`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_faemd/faemd2d.py) (Two-Dimensional Fast and Adaptive EMD) | [[paper]](https://ieeexplore.ieee.org/document/8447300) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/71270-fast-and-adaptive-multivariate-and-multidimensional-emd) | ✔️ |
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| [`FAEMD3D`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_faemd/faemd3d.py) (Three-Dimensional Fast and Adaptive EMD) | [[paper]](https://ieeexplore.ieee.org/document/8447300) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/71270-fast-and-adaptive-multivariate-and-multidimensional-emd) | ✔️ |
@@ -121,6 +120,7 @@ plot_IMFs(signal, IMFs) # per-channel panels
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| [`FMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_tid/fmd.py) (Feature Mode Decomposition) | [[paper]](https://ieeexplore.ieee.org/document/9732251) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/108099-feature-mode-decomposition-fmd) | ✔️ |
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| [`SSA`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_tid/ssa.py) (Singular Spectral Analysis) | [[paper]](https://orca.cardiff.ac.uk/id/eprint/15208/1/Zhiglavsky_SSA_encyclopedia.pdf) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/58967-singular-spectrum-analysis-beginners-guide) | ✔️ |
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| [`EWT`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_ewt/ewt.py) (Empirical Wavelet Transform) | [[paper]](https://ieeexplore.ieee.org/document/6522142) | [[code]](https://www.mathworks.com/help/wavelet/ug/empirical-wavelet-transform.html) | ✔️ |
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| [`EFD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_ewt/efd.py) (Empirical Fourier Decomposition) | [[paper]](https://www.sciencedirect.com/science/article/abs/pii/S0888327021005355) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/97747-empirical-fourier-decomposition-efd) | ✔️ |
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| [`EWT2D`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_ewt/ewt2d.py) (2D Empirical Wavelet Transform) | [[paper]](https://arxiv.org/abs/2405.06188) | [[code]](https://github.com/bhurat/EWT-Python) | ✔️ |
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| [`VMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_vmd/vmd_c.py) (Variational Mode Decomposition) | [[paper]](https://ieeexplore.ieee.org/document/6655981) | [[code]](https://github.com/vrcarva/vmdpy) | ✔️ |
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| [`MVMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_vmd/mvmd.py) (Multivariate Variational Mode Decomposition) | [[paper]](https://ieeexplore.ieee.org/document/8890883) | [[code]](https://github.com/yunyueye/MVMD) | ✔️ |
@@ -145,7 +145,7 @@ plot_IMFs(signal, IMFs) # per-channel panels
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| [`MJMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_jmd/mjmd.py) (Multivariate Jump Plus AM-FM Mode Decomposition) | [[paper]](https://arxiv.org/abs/2407.07800) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/169393-multivariate-jump-plus-am-fm-mode-decomposition-mjmd?s_tid=prof_contriblnk) | ✔️ |
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| [`SJMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_jmd/sjmd.py) / `SMJMD` (Successive Jump and Mode Decomposition) | [[paper]](https://arxiv.org/abs/2504.08453) | [[code]]() | ✔️ |
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| [`ESMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_emd/esmd.py) (Extreme-Point Symmetric Mode Decomposition) | [[paper]](https://arxiv.org/abs/1303.6540) | [[code]](https://github.com/WuShichao/esmd) | ✔️ |
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| [`STNBMD`]() (Short-Time Narrow-Band Mode Decomposition) | [[paper]](https://www.sciencedirect.com/science/article/pii/S0022460X16002443?via%3Dihub) | [[code]](https://ww2.mathworks.cn/matlabcentral/fileexchange/56226-short-time-narrow-band-mode-decomposition-stnbmd-toolbox) | ✔️ |
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| [`STNBMD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_vncmd/stnbmd.py) (Short-Time Narrow-Band Mode Decomposition) | [[paper]](https://www.sciencedirect.com/science/article/pii/S0022460X16002443?via%3Dihub) | [[code]](https://ww2.mathworks.cn/matlabcentral/fileexchange/56226-short-time-narrow-band-mode-decomposition-stnbmd-toolbox) | ✔️ |
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| [`VTFMTD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_tfa/vftmtd.py) (Variational TF Mode Tracking Decomposition) | [[paper]](https://www.sciencedirect.com/science/article/pii/S0165168426001179) | [[code]](https://www.mathworks.com/matlabcentral/fileexchange/183389-variational-time-frequency-mode-tracking-decomposition) | ✔️ |
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| [`SWD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_osd/swd.py) (Swarm Decomposition) | [[paper]](https://doi.org/10.1016/j.sigpro.2016.09.004) | [[code]](https://github.com/gkaposto/Swarm-Decomposition) | ✔️ |
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| [`OSD`](https://github.com/wwhenxuan/PySDKit/blob/main/pysdkit/_osd/osd.py) (Optimization-based Signal Decomposition) | [[paper]](https://web.stanford.edu/~boyd/papers/sig_decomp_mprox.html) | [[code]](https://github.com/cvxgrp/signal-decomposition) | ✔️ |

‎examples/acmd/acmd.ipynb‎

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@@ -339,13 +339,17 @@
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")\n",
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"if1 = 25 + 8 * t2 - 2.4 * t2**2 + 0.28 * t2**3\n",
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"\n",
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"c2 = 0.9 * np.exp(-0.06 * t2) * np.cos(\n",
343-
" 2 * np.pi * (2.6 + 40 * t2 + 8 * t2**2 - 1.6 * t2**3 + 0.14 * t2**4)\n",
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"c2 = (\n",
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" 0.9\n",
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" * np.exp(-0.06 * t2)\n",
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" * np.cos(2 * np.pi * (2.6 + 40 * t2 + 8 * t2**2 - 1.6 * t2**3 + 0.14 * t2**4))\n",
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")\n",
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"if2 = 40 + 16 * t2 - 4.8 * t2**2 + 0.56 * t2**3\n",
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"\n",
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"c3 = 0.8 * np.exp(-0.09 * t2) * np.cos(\n",
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" 2 * np.pi * (3.9 + 60 * t2 + 12 * t2**2 - 2.4 * t2**3 + 0.21 * t2**4)\n",
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"c3 = (\n",
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" 0.8\n",
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" * np.exp(-0.09 * t2)\n",
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" * np.cos(2 * np.pi * (3.9 + 60 * t2 + 12 * t2**2 - 2.4 * t2**3 + 0.21 * t2**4))\n",
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")\n",
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"if3 = 60 + 24 * t2 - 7.2 * t2**2 + 0.84 * t2**3\n",
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"\n",

‎examples/acmd/dd_acmd.ipynb‎

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‎examples/print_functions.ipynb‎

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‎pysdkit/__init__.py‎

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# Time Varying Filter based Empirical Mode Decomposition
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from ._emd import TVF_EMD
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# Empirical Fourier Decomposition
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from ._emd import EFD
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# Fast and Adaptive Empirical Mode Decomposition
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from ._faemd import FAEMD, FAEMD2D, FAEMD3D
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@@ -130,6 +127,9 @@
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# Empirical Wavelet Transform
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from ._ewt import ewt, EWT
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# Empirical Fourier Decomposition (spectrum segmentation + ideal filter bank)
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from ._ewt import efd, EFD
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# Empirical Wavelet Transform for 2D Images
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from ._ewt import ewt2d, EWT2D
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@@ -188,7 +188,6 @@ def print_functions():
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Multivariate Empirical Mode Decomposition | MEMD
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Serial Empirical Mode Decomposition | SEMD
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Time Varying Filter based EMD | TVF_EMD
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Empirical Fourier Decomposition | EFD
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Fast and Adaptive Empirical Mode Decomposition | FAEMD
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Bidimensional FAEMD | FAEMD2D
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Tridimensional FAEMD | FAEMD3D
@@ -223,6 +222,7 @@ def print_functions():
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Adaptive Polymorphic Mode Decomposition | APMD
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Impulsive Mode Decomposition | IMD
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Empirical Wavelet Transform | EWT
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Empirical Fourier Decomposition | EFD
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Empirical Wavelet Transform for 2D Image | EWT2D
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Jump Plus AM-FM Mode Decomposition | JMD
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Multivariate Jump Plus AM-FM Mode Decomposition | MJMD
@@ -245,7 +245,6 @@ def print_functions():
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"MEMD",
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"SEMD",
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"TVF_EMD",
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"EFD",
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"FAEMD",
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"FAEMD2D",
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"FAEMD3D",
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"imd",
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"ewt",
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"EWT",
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"efd",
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"EFD",
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"ewt2d",
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"EWT2D",
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"JMD",

‎pysdkit/_acmd/acmd.py‎

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win_len = int(np.ceil(win_len / 2.0) * 2)
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t_win = np.linspace(-1.0, 1.0, win_len)
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sigma = 0.28
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win_fun = (np.pi * sigma**2) ** (-0.25) * np.exp((- (t_win**2)) / (2.0 * sigma**2))
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win_fun = (np.pi * sigma**2) ** (-0.25) * np.exp((-(t_win**2)) / (2.0 * sigma**2))
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lh = (win_len - 1) / 2.0
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spec = np.zeros((n_fft, sig_len), dtype=complex)
@@ -199,9 +199,9 @@ def _spsolve_safe(a, b: np.ndarray) -> np.ndarray:
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"""Sparse solve with dense lstsq fallback (MATLAB ``\\`` robustness)."""
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x = spsolve(a, b)
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if not np.all(np.isfinite(x)):
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x = np.linalg.lstsq(a.toarray(), np.asarray(b, dtype=float).ravel(), rcond=None)[
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0
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]
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x = np.linalg.lstsq(
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a.toarray(), np.asarray(b, dtype=float).ravel(), rcond=None
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)[0]
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return np.asarray(x, dtype=float).ravel()
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return peak_fre * np.ones(N, dtype=float)
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@staticmethod
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def differ(
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y: np.ndarray, delta: float, dtype: np.dtype = np.float64
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) -> np.ndarray:
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def differ(y: np.ndarray, delta: float, dtype: np.dtype = np.float64) -> np.ndarray:
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"""Instance-accessible wrapper around module-level ``differ``."""
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out = differ(y, delta)
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return np.asarray(out, dtype=dtype)

‎pysdkit/_acmd/ba_acmd.py‎

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@@ -81,9 +81,7 @@ def gini_squared_envelope(signal: np.ndarray) -> float:
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return float(1.0 - 2.0 * temp / (np.linalg.norm(se, 1) + np.finfo(float).eps))
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def extract_if_ia(
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y: np.ndarray, fs: float
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) -> Tuple[np.ndarray, np.ndarray]:
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def extract_if_ia(y: np.ndarray, fs: float) -> Tuple[np.ndarray, np.ndarray]:
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"""
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Instantaneous frequency / amplitude via padded analytic signal
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(MATLAB ``IFIAextrc``).
@@ -190,15 +188,11 @@ def coef_overcomplete_fourier(
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if (j + 1) > half:
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k = (j + 1) - half
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tmatrix_inte[:, j] = (
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-1.0
194-
/ (2.0 * np.pi * f0 * k)
195-
* np.cos(2.0 * np.pi * f0 * k * dt)
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-1.0 / (2.0 * np.pi * f0 * k) * np.cos(2.0 * np.pi * f0 * k * dt)
196192
)
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198194
eye_m = np.eye(order_amp)
199-
coeff = np.linalg.solve(
200-
alpha * eye_m + tmatrix.T @ tmatrix, tmatrix.T @ f
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)
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coeff = np.linalg.solve(alpha * eye_m + tmatrix.T @ tmatrix, tmatrix.T @ f)
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fitf = tmatrix @ coeff
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finte = tmatrix_inte @ coeff
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return fitf, finte
@@ -232,9 +226,7 @@ def spectrum_trend_generate(
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# Local minima of the spectrum trend
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minima, _ = find_peaks(-spec_trend)
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temp_index = np.concatenate(
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([0], minima.astype(int), [freq_bin.size - 1])
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)
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temp_index = np.concatenate(([0], minima.astype(int), [freq_bin.size - 1]))
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temp_frn = temp_index[:-1]
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temp_end = temp_index[1:]

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