Wav-KAN is a novel neural network architecture that integrates wavelet functions into the Kolmogorov-Arnold Networks (KAN) framework to enhance interpretability and performance. Traditional models like MLPs and Spl-KAN face challenges in interpretability, training speed, robustness, and efficiency. Wav-KAN addresses these by using wavelet functions to capture both high and low-frequency components of input data efficiently. Wavelet-based approximations use orthogonal or semi-orthogonal basis functions, balancing data structure representation and noise avoidance. Discrete wavelet transform (DWT) enables efficient multiresolution analysis, avoiding redundant calculations and combining local details with broader trends. Wav-KAN adapts to data structure, resulting in improved accuracy, faster training, and robustness compared to Spl-KAN and MLPs. The framework is versatile, applicable across various fields, and can be implemented in PyTorch, TensorFlow, and R. Wav-KAN's wavelet-based approach offers a balance between function approximation and noise avoidance, making it a powerful tool for interpretable and high-performance neural networks. The paper introduces Wav-KAN, demonstrating its effectiveness in tasks like image recognition and signal processing. It also highlights the potential of wavelets in KANs, similar to how ReLU and sigmoid are used in universal approximation theory. The results show that Wav-KAN outperforms Spl-KAN and MLPs in terms of accuracy and training speed, with efficient parameter usage and improved interpretability. The framework is designed to handle high-dimensional data and provide clear insights into model behavior, making it a promising tool for scientific research and industrial applications. Future work will focus on optimizing Wav-KAN and exploring its applicability to other datasets and tasks.Wav-KAN is a novel neural network architecture that integrates wavelet functions into the Kolmogorov-Arnold Networks (KAN) framework to enhance interpretability and performance. Traditional models like MLPs and Spl-KAN face challenges in interpretability, training speed, robustness, and efficiency. Wav-KAN addresses these by using wavelet functions to capture both high and low-frequency components of input data efficiently. Wavelet-based approximations use orthogonal or semi-orthogonal basis functions, balancing data structure representation and noise avoidance. Discrete wavelet transform (DWT) enables efficient multiresolution analysis, avoiding redundant calculations and combining local details with broader trends. Wav-KAN adapts to data structure, resulting in improved accuracy, faster training, and robustness compared to Spl-KAN and MLPs. The framework is versatile, applicable across various fields, and can be implemented in PyTorch, TensorFlow, and R. Wav-KAN's wavelet-based approach offers a balance between function approximation and noise avoidance, making it a powerful tool for interpretable and high-performance neural networks. The paper introduces Wav-KAN, demonstrating its effectiveness in tasks like image recognition and signal processing. It also highlights the potential of wavelets in KANs, similar to how ReLU and sigmoid are used in universal approximation theory. The results show that Wav-KAN outperforms Spl-KAN and MLPs in terms of accuracy and training speed, with efficient parameter usage and improved interpretability. The framework is designed to handle high-dimensional data and provide clear insights into model behavior, making it a promising tool for scientific research and industrial applications. Future work will focus on optimizing Wav-KAN and exploring its applicability to other datasets and tasks.