IEEE Transactions on Signal Processing
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The conventional complete discrete wavelet transform (DWT) is shift-sensitive, so that the analysis often becomes unstable. In this paper, we define a measure of shift-sensitivity, based on which we propose a new DWT less sensitive than the complete DWT. The measure is derived from the normalized variation of the output waveform for a shifted signal. The measure indicates that a narrow-band high-pass filter is desirable for shift-insensitivity. Then we propose a new DWT which makes use of a complex filter with half bandwidth of a high-pass filter of an ordinary DWT. In two dimensions, the proposed DWT can decompose an image into either four or six directional components which include two separate diagonals, while the complete DWT decomposes the image into three directional components. We show the effectiveness of our method by evaluating the shift-sensitivity of our DWT and other DWTs. By our DWT a smooth continuing edge of an image can be detected, but by the complete DWT a discontinuous edge is produced.