Wavelet Analysis

Wavelet Analysis is a signal processing technique that decomposes data into time-frequency components — unlike Fourier analysis (which shows only frequencies), wavelets show when specific frequencies occur, making them ideal for non-stationary semiconductor process signals.

How Do Wavelets Work?

• Mother Wavelet: A short oscillatory function (e.g., Daubechies, Morlet, Haar) that is scaled and shifted.
• Multiresolution: Decompose the signal at multiple scales simultaneously (coarse trends + fine details).
• Time-Frequency: Each wavelet coefficient represents a specific frequency at a specific time.
• Thresholding: Wavelet denoising removes noise by thresholding small coefficients.

Why It Matters

• Non-Stationary Signals: Process signals that change character over time (transients, excursions) are better handled by wavelets than FFT.
• Denoising: Wavelet denoising preserves sharp features (edges, transients) better than moving average or Fourier filtering.
• Fault Detection: Transient equipment faults appear as localized wavelet features, easily detected.

Wavelet Analysis is the time-frequency microscope — simultaneously resolving both when and what frequency events occur in process data.