离散傅里叶变换在卷积神经网络中能够显著加速卷积的计算。此外，频域可能也为训练与构建卷积神经网络提供了一种有力的表征方法。 在这一工作中，我主要讨论了频域表征在不同问题及方向下的应用并且对于CNN的设计提出了一些创新。 我基于自然图像(eg.CIFAR-10数据集)与非自然图像(eg.MNIST数据集)进行研究，并提出了概率权重频域池化，并比对了中心频域池化及概率权重频域池化。灵活的采用这两种方法可以应对的不同分类问题。频域池化相对于传统的时域池化方法（eg.Max pooling,stochastic pooling等）应该说被认为在单个变量上能够保留更多的信息。我展示了在图像分类任务中采用这两种方法的卷积神经网络能够达到具有竞争力的结果。

Discrete Fourier Transforms(DFT) can speedup the computation of convolutions in Convolutional Neuron Network(CNN).Besides,Spectral domain maybe also provide a powerful representation for model and train CNN. In this work,I discuss the application of Spectral Representation in different problems and directions and introduce some innovations to CNN design. I work with Natural Image(eg.CIFAR-10 dataset)and Artificial Image(eg.MNIST dataset),and propose Central Spectral Pooling and Probability Weighted Spectral Pooling .Apply those two method flexibly can handle different classfication problem.Spectral pooling should be considered to preserve more information per parameter comparing with conventional spatial pooling methods(eg.Max pooling,Stochastic Pooling).I show that CNNs with those two method can achieve competitive results on image classification tasks.