Recent advancements in machine learning and deep learning have witnessed profound growth in their accuracy, particularly in classification. The improvement in accuracy also increases the complexity of the network. The increasing complexity of such learning models has resulted in them being termed “black boxes". The imperative need of the hour is to ensure that these models are highly accurate, interpretable, and transparent, especially in critical applications like biometric identification. However, the research focusing on the explainability of these models has been relatively limited. In recent years, a shift has been observed where researchers are increasingly delving into enhancing the explainability of machine learning and deep learning algorithms. This paper sheds light on pivotal elements from the wavelet domain that aim to incorporate economy and explainability in deep learning, spanning classification, and generative modeling tasks, with a particular emphasis on biometric applications. An innovative concept introduced in this paper is the Shearlet-based Feature Attention (SFA) and Contourlet-based Feature Attention (CFA). Rooted in signal processing, the SFA and CFA techniques emphasize the attention allocated to different features based on frequency details concerning the spatial domain. Notably, the SFA has not only surpassed some of the already existing models in biometric applications but has also achieved a commendable feat by ensuring more than 50% economy in convolutional layers with more than 33% increase in model performance.