<p>Recent advances in convolutional neural networks (CNNs) have significantly improved visual recognition performance. However, most existing architectures rely on deep and heavily parameterized models that suffer from limited interpretability and high computational cost. In this work, we propose BetaWave-CNN, a lightweight and explainable architecture that replaces randomly initialized convolution kernels with analytically defined and parameterized Beta-wavelet filters. By optimizing only the wavelet shape parameters, the proposed model reduces the number of effective trainable parameters while preserving multiscale representational capability. To further improve robustness and information preservation, we introduce WavePool, a learnable wavelet-based pooling mechanism that performs smooth multi-resolution aggregation with controlled computational overhead. The proposed architecture was evaluated on five benchmark datasets of increasing complexity: MNIST, Kuzushiji-MNIST, EMNIST, SVHN, and LFW. Experimental results demonstrate that BetaWave-CNN achieves competitive or superior performance using shallow architectures of only 2–6 convolutional layers, reaching accuracies of 98.72% on MNIST, 91.34% on KMNIST, 97.00% on EMNIST, 97.80% on SVHN, and 99.21% on LFW (under the restricted protocol). In addition to its classification performance, the proposed model exhibits strong computational efficiency, requiring as little as 2.08 MFLOPs for MNIST-scale inputs and remaining fully executable on a CPU-only platform without GPU acceleration. Compared with conventional CNNs and existing wavelet-based approaches, BetaWave-CNN offers a favorable trade-off between accuracy, interpretability, and computational complexity. These results position the proposed architecture as a sustainable, explainable, and resource-efficient alternative aligned with the principles of Green AI and Frugal AI.</p>