Frequency domain complex-valued convolutional neural network

• Formulation of fully complex-valued building blocks for complex-valued CNNs, ensuring consistent operation in the frequency domain. • Lightweight, computationally efficient, fully complex-valued residual CNN operating on complex data in the frequency domain. • Novel log-magnitude activation function that maintains phase information while introducing effective non-linearity, along with a detailed comparative analysis with the complex ReLU variant and the Cardioid activation function. • We have shown that complex-valued CNNs can outperform real-valued CNNs, enhancing performance and generalization while reducing computational demands. Complex-valued convolutional neural networks have demonstrated promising results in reducing space, time, and computational complexity compared to real-valued models, particularly in signal and image processing. Despite their strong representational capacity and theoretical benefits, complex-valued CNNs remain limited due to theabsence of simplified theoretical and practical formulations for fully complex-valued building blocks. Existing studies often depend on fast Fourier transforms (FFT/IFFT) for domain transitions between layers due to the lack of well-established complex-valued activation functions or filter parameters initialization. Additionally, many earlier works adapt complex versions of the real-valued activation functions in a split-type manner, which might distort phase information and weaken generalization. To overcome these challenges, we propose a lightweight fully complex-valued residual CNN that operates entirely on complex data in the frequency domain. Our design simplifies fully complex building blocks and introduces a Log-Magnitude activation function that preserves phase information, outperforming traditional complex ReLU variants and the Cardioid activation function. Experimental validation across diverse multi-modal datasets, including MNIST, SVHN, MIT-BIH Arrhythmia, PTB Diagnostic ECG, DIAT- μ RadHAR , and DIAT- μ SAT , demonstrates the superior performance of our fully complex-valued CNNs over real-valued models.