This article proposes a novel spectral domain based solution to the challenging polyp segmentation. The main contribution is based on an interesting finding of the significant existence of the middle frequency sub-band during the CNN process. Consequently, a Sub-Band based Attention (SBA) module is proposed, which uniformly adopts either the high or middle sub-bands of the encoder features to boost the decoder features and thus concretely improve the feature discrimination. A strong encoder supplying informative sub-bands is also very important, while we highly value the local-and-global information enriched CNN features. Therefore, a Transformer Attended Convolution (TAC) module as the main encoder block is introduced. It takes the Transformer features to boost the CNN features with stronger long-range object contexts. The combination of SBA and TAC leads to a novel polyp segmentation framework, SBA-Net. It adopts TAC to effectively obtain encoded features which also input to SBA, so that efficient sub-bands based attention maps can be generated for progressively decoding the bottleneck features. Consequently, SBA-Net can achieve the robust polyp segmentation, as the experimental results demonstrate.