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Digital filtering of images using the discrete sine or cosine transform

The discrete sine and cosine transforms (DSTs and DCTs) are powerful tools for image compression. They would be even more useful if they could be used to perform convolution. As we have recently shown, these transforms do possess a convolution-multiplication property and therefore can be used to perform digital filtering. The convolution is a special type, called symmetric convolution. This paper reviews the concepts of symmetric convolution then elaborates on how to use the operation, and therefore DSTs and DCTs, to implement digital filters for images. An indication of how to compute the transforms and what is the complexity of their use is also given.