Neural front-ends represent a promising approach to feature extraction for automatic speech recognition (ASR) systems as they enable to learn specifically tailored features for different tasks. Yet, many of the existing techniques remain heavily influenced by classical methods. While this inductive bias may ease the system design, our work aims to develop a more generic front-end for feature extraction. Furthermore, we seek to unify the front-end architecture contrasting with existing approaches that apply a composition of several layer topologies originating from different sources. The experiments systematically show how to reduce the influence of existing techniques to achieve a generic front-end. The resulting 2D convolutional front-end is parameter-efficient and suitable for a scenario with limited computational resources unlike large models pre-trained on unlabeled audio. The results demonstrate that this generic unified approach is not only feasible but also matches the performance of existing supervised learnable feature extractors.