Convolutional Fourier Analysis Network (CFAN): A Unified Time-Frequency Approach for ECG Classification

Machine learning has revolutionized biomedical signal analysis, particularly in electrocardiogram (ECG) classification. While convolutional neural networks (CNNs) excel at automatic feature extraction, the optimal integration of time- and frequency-domain information remains unresolved. This study introduces the Convolutional Fourier Analysis Network (CFAN), a novel architecture that unifies time-frequency analysis by embedding Fourier principles directly into CNN layers. We evaluate CFAN against four benchmarks - spectrogram-based 2D CNN (SPECT); 1D CNN (CNN1D); Fourier-based 1D CNN (FFT1D); and CNN1D with integrated Fourier Analysis Network (CNN1D-FAN) - across three ECG tasks: arrhythmia classification (MIT-BIH), identity recognition (ECG-ID), and apnea detection (Apnea-ECG). CFAN achieved state-of-the-art performance, surpassing all competing methods with accuracies of 98.95% (MIT-BIH), 96.83% (ECG-ID), and 95.01% (Apnea-ECG). Notably, on ECG-ID and Apnea-ECG, CFAN demonstrated statistically significant improvements over the second-best method (CNN1D-FAN, $p \leq 0.02$), further validating its superior performance. Key innovations include CONV-FAN blocks that combine sine, cosine and GELU activations in convolutional layers to capture periodic features and joint time-frequency learning without spectrogram conversion. Our results highlight CFAN's potential for broader biomedical and signal classification applications.