CWT Scalogram Analysis for PPG
The Continuous Wavelet Transform (CWT) convolves the PPG signal with scaled and shifted wavelet functions across a continuous range of scales, producing a scalogram with adaptive time-frequency resolution — high frequency resolution at low frequencies (respiratory band) and high time resolution at high frequencies (cardiac harmonics).
CWT coefficients W(a,b) = ∫ x(t)·(1/√a)·ψ*((t-b)/a)dt represent the correlation between the PPG signal and scaled wavelets at scale a and position b. The scale-frequency relationship f = f_c/(a·Δ) maps wavelet scales to pseudo-frequencies. The Morlet wavelet (complex sinusoid modulated by Gaussian) is widely used for PPG because it provides excellent frequency localization while maintaining compact temporal support.
CWT scalograms of PPG clearly visualize the cardiac rhythm as a high-energy ridge at the fundamental frequency, with harmonics visible as parallel ridges at 2×, 3× the fundamental. Ridge extraction algorithms trace the instantaneous cardiac frequency along the maximum-energy path in the scalogram, providing continuous heart rate estimation that is robust to transient artifacts because artifacts create disconnected energy regions rather than continuous ridges.
For deep learning applications, CWT scalograms serve as 2D image inputs to CNN classifiers trained for AF detection, sleep staging, and stress classification. The time-frequency image representation enables transfer learning from pretrained image classification networks (ResNet, EfficientNet) to PPG classification tasks, achieving 2–5% accuracy improvement over raw 1D waveform inputs in several benchmarks.
Frequently Asked Questions
How does CWT compare to DWT for PPG?
CWT provides continuous scale coverage for smooth frequency tracking, while DWT operates at dyadic scales (powers of 2). CWT is preferred for spectrogram-based analysis and visualization; DWT is preferred for signal decomposition and reconstruction due to non-redundancy.
What wavelet is best for PPG CWT?
Complex Morlet wavelet (bandwidth parameter 1–2, center frequency 1) provides optimal balance between time and frequency resolution for cardiac frequency tracking. Mexican hat wavelet is effective for beat detection as it matches the systolic peak shape.
Is CWT computationally feasible for real-time PPG?
CWT at all scales is computationally expensive (O(N²)). Restricting scales to the cardiac band (0.5–4 Hz) and using fast CWT implementations (filter bank approach) reduces computation to O(N·K) where K is the number of scales, feasible on embedded processors.