The discreteW transform

Four different versions of the discreteW transform (DWT) are introduced. The DWT may be decomposed into the discrete cosine transform (DCT) and the discrete sine transform (DST). Eight versions of both DCT and DST are introduced for the decomposition of the DWT. The relationship among different versions of DWT and their relation with the discrete Fourier transform (DFT) are given. Convolution theorems represented by different versions of the DWT are derived.