Short-time Variational Mode Decomposition (STVMD)

Python implementation of Short-time Variational Mode Decomposition (STVMD) algorithm, as described in our paper "Short-time Variational Mode Decomposition".

Overview

STVMD extends traditional Variational Mode Decomposition (VMD) by incorporating Short-Time Fourier Transform (STFT) for analyzing non-stationary signals. The method comes in two variants:

• Non-dynamic STVMD: Uses fixed central frequencies across time windows
• Dynamic STVMD: Allows central frequencies to vary with time

Requirements

numpy
scipy
numba
matplotlib
tqdm
emd-signal

Usage

Basic example:

from stvmd import STVMD

# Initialize STVMD
stvmd = STVMD(
    num_channel=1,      # Number of input channels
    n_fft=64,          # FFT size
    alpha=50,          # Balancing parameter
    K=3,               # Number of modes
    tol=1e-9,         # Convergence tolerance
    tau=0.00001       # Update step size
)

# Prepare data
f_hat_s, b_hat_s = stvmd.prepare_offline(signal)

# Apply decomposition
# For non-dynamic STVMD:
u_hat_s, w_hat_s = stvmd.apply(f_hat_s, dynamic=False)

# For dynamic STVMD:
u_hat_s, w_hat_s = stvmd.apply(f_hat_s, dynamic=True)

# Get mode functions
imf_stvmd = stvmd.postprocess(u_hat_s)

See paste.txt for complete implementation and examples.

Citation

If you use this code in your research, please cite:

@article{jia_short-time_2025,
	title = {Short-time variational mode decomposition},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {0165-1684},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0165168425003172},
	doi = {10.1016/j.sigpro.2025.110203},
	language = {en},
	urldate = {2025-07-24},
	journal = {Signal Processing},
	author = {Jia, Hao and Cao, Pengfei and Liang, Tong and Caiafa, Cesar F. and Sun, Zhe and Kushihashi, Yasuhiro and Grau, Antoni and Bolea, Yolanda and Duan, Feng and Solé-Casals, Jordi},
	month = jul,
	year = {2025},
	note = {Publisher: Elsevier BV},
	pages = {110203},
}

License

MIT License

References

• Original VMD paper: Dragomiretskiy, K., & Zosso, D. (2014). Variational mode decomposition. IEEE transactions on signal processing, 62(3), 531-544.
• MVMD paper: Rehman, N., & Aftab, H. (2019). Multivariate variational mode decomposition. IEEE Transactions on Signal Processing, 67(23), 6039-6052.