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In this paper, we prove the representation defects of a cascadedconvolutional decoder network, considering the capacity of representingdifferent frequency components of an input sample. We conduct the discreteFourier transform on each channel of the feature map in an intermediate layerof the decoder network. Then, we extend the 2D circular convolution theorem torepresent the forward and backward propagations through convolutional layers inthe frequency domain. Based on this, we prove three defects in representingfeature spectrums. First, we prove that the convolution operation, thezero-padding operation, and a set of other settings all make a convolutionaldecoder network more likely to weaken high-frequency components. Second, weprove that the upsampling operation generates a feature spectrum, in whichstrong signals repetitively appear at certain frequencies. Third, we prove thatif the frequency components in the input sample and frequency components in thetarget output for regression have a small shift, then the decoder usuallycannot be effectively learned.

Defects of Convolutional Decoder Networks in Frequency Representation