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As much as Graph Convolutional Networks (GCNs) have shown tremendous success in recommender systems and collaborative filtering (CF), the mechanism of how they, especially the core components (\textit{i.e.,} neighborhood aggregation) contribute to recommendation has not been well studied. To unveil the effectiveness of GCNs for recommendation, we first analyze them in a spectral perspective and discover two important findings: (1) only a small portion of spectral graph features that emphasize the neighborhood smoothness and difference contribute to the recommendation accuracy, whereas most graph information can be considered as noise that even reduces the performance, and (2) repetition of the neighborhood aggregation emphasizes smoothed features and filters out noise information in an ineffective way. Based on the two findings above, we propose a new GCN learning scheme for recommendation by replacing neihgborhood aggregation with a simple yet effective Graph Denoising Encoder (GDE), which acts as a band pass filter to capture important graph features. We show that our proposed method alleviates the over-smoothing and is comparable to an indefinite-layer GCN that can take any-hop neighborhood into consideration. Finally, we dynamically adjust the gradients over the negative samples to expedite model training without introducing additional complexity. Extensive experiments on five real-world datasets show that our proposed method not only outperforms state-of-the-arts but also achieves 12x speedup over LightGCN.