Wavelet Threshold Denoising: A Time-Scale (Time-Frequency) Analysis Method for Signals

Wavelet threshold denoising is a signal denoising method based on wavelet transform that leverages the multi-resolution analysis properties of wavelet transforms to simultaneously display signal characteristics in both time and frequency domains. This approach effectively separates noise from useful signals by analyzing signal behavior across different scales. In implementation, this typically involves decomposing the signal using discrete wavelet transform (DWT) functions like wavedec() in MATLAB or pywt.wavedec() in Python's PyWavelets library.

The advantage of wavelet transform lies in its multi-scale characteristics, which decompose signals into different frequency bands, each corresponding to different time resolutions. During the denoising process, thresholding is applied to wavelet coefficients to preserve main signal components while suppressing noise interference. Common threshold strategies include hard thresholding (completely eliminating coefficients below threshold) and soft thresholding (shrinking coefficients toward zero), which can be flexibly selected based on signal characteristics using functions such as wthresh() in signal processing toolboxes.

Wavelet threshold denoising is widely applied in image processing, biomedical signal analysis, and vibration signal detection, particularly suitable for denoising non-stationary signals. Since wavelet transforms effectively capture transient signal features, this method significantly improves the signal-to-noise ratio while preserving signal details. Practical implementations often involve choosing optimal wavelet families (like Daubechies or Symlets) and determining thresholds using methods such as universal threshold or minimax threshold through algorithms like wden() or wdencmp() in computational environments.