Interpretability often seeks domain-specific facts, which is understandable to human, from deep-learning (DL) or other machine-learning (ML) models of black-box nature. This is particularly important to establish transparency in ML model’s inner-working and decision-making, so that a certain level of trust is achieved when a model is deployed in a sensitive and mission-critical context, such as health-care. Model-level transparency can be achieved when its components are transparent and are capable of explaining reason of a decision, for a given input, which can be linked to domain-knowledge. This article used convolutional neural network (CNN), with sinc-convolution as its constrained first-layer, to explore if such a model’s decision-making can be explained, for a given task, by observing the sinc-convolution’s sinc-kernels. These kernels work like band-pass filters, having only two parameters per kernel - lower and upper cutoff frequencies, and optimised through back-propagation. The optimised frequency-bands of sinc-kernels may provide domain-specific insights for a given task. For a given input instance, the effects of sinc-kernels was visualised by means of explanation vector, which may help to identify comparatively significant frequency-bands, that may provide domain-specific interpretation, for the given task. In addition, a CNN model was further optimised by considering the identified subset of prominent sinc frequency-bands as the constrained first-layer, which yielded comparable or better performance, as compared to its all sinc-bands counterpart, as well as, a classical CNN. A minimal CNN structure, achieved through such an optimisation process, may help design task-specific interpretable models. To the best of our knowledge, the idea of sinc-convolution layer’s task-specific significant sinc-kernel-based network optimisation is the first of its kind. Additionally, the idea of explanation-vector-based joint time-frequency representation to analyse time-series signals is rare in the literature. The above concept was validated for two tasks, ECG beat-classification (five-class classification task), and R-peak localisation (sample-wise segmentation task).