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.