Dual-tree complex wavelet transform arising from cosine-sine modulated filter banks

The purpose of this paper is to show an another design approach of the M-band dual-tree complex wavelet transform (DTCopfWT). Conventionally, M-channel cosine-sine modulated filter bank has been proposed as an extension of cosine modulated filter bank. It can be easily designed by the modulation of one prototype filter. In this paper, we show that it can be regarded as an alternative DTCopfWT with respect to its relationship to the analyticity. In addition, we also present its shift-invariance, rich directional selectivity which are effective for the image processing. Therefore it can provide the simple design of M-band DTCopfWT. In this paper, these properties are verified by theoretical analysis and demonstrations.