Wavelet Neural Networks: Integrating Wavelet Analysis with Neural Network Architectures

This article introduces Wavelet Neural Networks (WNNs), an innovative methodology that integrates wavelet analysis with neural network architectures by substituting conventional activation functions with wavelet basis functions. WNNs demonstrate extensive applicability across diverse domains including signal processing, image analysis, and pattern recognition systems. The principal advantage of wavelet neural networks lies in their capacity to simultaneously capture time-frequency characteristics while maintaining superior localization properties. This integration provides enhanced computational tools for addressing complex problems, significantly improving data interpretation and analytical capabilities. From an implementation perspective, WNNs typically involve constructing wavelet neurons where the activation function is replaced by orthogonal or non-orthogonal wavelet families (e.g., Morlet, Mexican Hat wavelets), often implemented through customized TensorFlow/PyTorch layers with trainable dilation and translation parameters.