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3. Examples
To illustrate the use of the discrete wavelet transform, let's consider image compression. In the case of images, we use the discrete wavelet transform in two dimensions (2D), which is a generalization of the one-dimensional case (1D).
In the following examples, we consider the image as a 2D arrangement. We take the 2D discrete wavelet transform using a recursive relationship similar to
(48)
. We use an 8th-order filter, which has been designed to match the
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