This paper implements the discrete wavelet transform in the discrete Fourier domain. The need for such an approach arose out of our desire to find a convenient means of realizing a new class of non-separable orientation selective 2-D wavelet filter hanks that are designed directly in the DFT domain. The filter bank design process begins with a conventional separable 2-D perfect reconstruction parallel filter bank that is not orientation selective. In the D I T domain; each non-low pass channel

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... s decomposed into the sum of two orientation selective frequency responses that are each supported on only two quadnnts of the 2-D frequency plane. The resulting filter bank possesses the good joint localization properties of orthogonal wavelet transforms and offers both perfect reconstruction and orientation selectivity. However, the orientation selective channels are non-separablethey cannot be implemented as iterated 1-D convolutions according to the usual separable 2-D wavelet transform paradigm. To overcome this difficulty, we develop straightforward techniques for implemening the DWT directly in the DFT domain. 0-7803-8387-7/04/$20.00 0 2004 IEEE