Enhancing CNN-Based Signal Denoising: A Novel Metric Framework With Harmonic Suppression Through Hybrid Modeling

Convolutional neural networks (CNNs) show promise for signal denoising but can introduce harmonic distortions due to their nonlinearity. This paper introduces a comprehensive evaluation framework that merges traditional metrics like Signal-to-Noise Ratio (SNR) and Mean Squared Error (MSE) with proposed harmonic power-related metrics: Fundamental Power Ratio (FPR), Fundamental to Total Harmonic Power ratio (FTHPR), and Harmonic Power Ratio (HPR) to analyze the performance and generalization of four CNN architectures: Denoising Convolutional Neural Network (DnCNN), Deep Convolutional Neural Network (DCNN), Deep Convolutional Autoencoder (DDCAE), and a hybrid Convolutional Neural Network - Long Short-Term Memory (CNN-LSTM) model. The models were trained on sinusoids with white noise and tested under in-distribution, out-of-distribution (OOD) colored noise (pink/blue, lower SNRs) and real-world signal conditions. The results show that while DDCAE is computationally efficient and performs well in distribution, it struggles with excessive harmonic generation under OOD/real-world conditions. CNN-LSTM demonstrates superior spectral purity and generalization across synthetic colored noises. However, DCNN exhibits greater robustness in complex real-world signals and under extremely low SNR synthetic conditions, effectively handling noise and harmonic distortions where other models falter. A proposed hybrid model (post-CNN linear filter) generally improved performance, particularly by mitigating harmonic issues for models like DDCAE. These findings highlight significant performance trade-offs and demonstrate that the optimal model choice is highly context-dependent (noise type, SNR, computational budget). Comprehensive out-of-distribution evaluations and metrics that account for harmonic content are essential for choosing dependable denoising models in real-world settings.