2-D Discrete-Space Transforms
In this chapter we look at discrete-space transforms such as discrete Fourier series, discrete Fourier transform (DFT), and discrete cosine transform (DCT) in two dimensions. We also discuss fast and efficient realizations of the DFT and DCT. The DFT is a heavily used tool in image and multidimensional signal processing. Block transforms can be obtained from scanning the data into small blocks and then performing the DFT or DCT on each block. The block DCT is used extensively in image and video compression for transmission and storage. We also consider the subband/wavelet transform (SWT), which can be considered as a generalization of the block DCT transform wherein the basis functions are allowed to ...
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