The choice of an optimal time-frequency resolution is usually a difficult but important step in tasks involving speech signal classification, e.g., speech anti-spoofing. The variations of the performance with different choices of timefrequency resolutions can be as large as those with different model architectures, which makes it difficult to judge what the improvement actually comes from when a new network architecture is invented and introduced as the classifier. In this paper, we propose a multi-resolution front-end for feature extraction in an end-to-end classification framework. Optimal weighted combinations of multiple time-frequency resolutions will be learned automatically given the objective of a classification task. Features extracted with different time-frequency resolutions are weighted and concatenated as inputs to the successive networks, where the weights are predicted by a learnable neural network inspired by the weighting block in squeeze-and-excitation networks (SENet). Furthermore, the refinement of the chosen timefrequency resolutions is investigated by pruning the ones with relatively low importance, which reduces the complexity and size of the model. The proposed method is evaluated on the tasks of speech anti-spoofing in ASVSpoof 2019 and its superiority has been justified by comparing with similar baselines.