Wavelet Decomposition in PPG Signal Processing
Wavelet decomposition decomposes a PPG signal into time-frequency components by correlating the signal with scaled and shifted wavelet basis functions, providing simultaneous time and frequency resolution superior to the short-time Fourier transform for analyzing the non-stationary, quasi-periodic PPG signal.
The Discrete Wavelet Transform (DWT) decomposes a PPG signal through a bank of half-band low-pass and high-pass filters, producing approximation (low-frequency) and detail (high-frequency) coefficients at each decomposition level. A 6-level DWT of a PPG sampled at 125 Hz separates the signal into bands: level 6 approximation (0–2 Hz, cardiac band), level 5 details (2–4 Hz, second harmonic), level 4 details (4–8 Hz, motion/respiration), and higher levels capturing high-frequency noise.
For PPG baseline wander correction, a standard approach zeros all approximation coefficients at decomposition levels 6–9 (depending on sampling rate) before reconstructing the signal. This removes slow baseline drift (< 0.5 Hz) without distorting the pulse waveform shape. Stationary Wavelet Transform (SWT), which avoids downsampling at each level, is preferred for baseline correction to prevent Gibbs artifacts at level boundaries.
Motion artifact removal using wavelets works best when the cardiac and motion frequencies are well-separated. Decomposition levels containing motion energy are identified using accelerometer signal correlation and zeroed or thresholded in the PPG wavelet domain before reconstruction. Rigorous thresholding rules — hard thresholding (zero coefficients below threshold), soft thresholding (shrink towards zero), and Stein's unbiased risk estimate (SURE) threshold — balance noise removal against cardiac signal preservation.
Frequently Asked Questions
Which wavelet basis is best for PPG processing?
Daubechies (db4–db8) wavelets are most widely used for PPG due to their compact support and near-symmetry, which minimizes phase distortion. Symlets (sym4–sym8) offer improved symmetry. Biorthogonal wavelets allow independent control of analysis and synthesis filter shapes.
How does wavelet decomposition compare to Fourier transform for PPG?
Fourier provides global frequency information but no temporal localization. Wavelets provide time-frequency localization, making them superior for analyzing PPG segments with transient artifacts, beat detection, and non-stationary rhythm analysis.
Can wavelets detect PPG beats better than simple peak picking?
Yes. Mexican hat wavelet (second derivative of Gaussian) correlation with PPG is equivalent to matched filtering for the systolic peak and provides robust detection under moderate noise conditions, achieving F1 > 0.97 across multiple PPG quality levels in standard benchmarks.