A true continuous wavelet transform (CWT) must be continuous in both shift and scale. By a continuous anamorphic transformation of a one-dimensional (1D) signal and a suitable choice of kernel or filter, we can allow a normal two-dimensional (2D) optical Fourier transform image processor to perform a CWT.
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H. John Caulfield, Harold H. Szu, "Continuous wavelet transform of 1D signals by Fourier filtering," Proc. SPIE 1705, Visual Information Processing, (1 October 1992);