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2-D DFT of two dimensional finite extent sequences.

2-D DFT and Convolution
The DFT can be computed with a fast algorithm and it is sometimes beneficial to do the convolution of two sequences A (M1 £ N1) and B (M2 £ N2) via [M1 +M2 + 1;N1 + N2 + 1] point DFTs. Speed improvements are only possible if both sequences have large dimensions. Otherwise convolutions are better implemented via the convolution sum.

2-D Low-Pass Filtering of Images We will be interested in two ways of implementing low-pass filtering for images: ² By defining “windows” in the DFT domain, selecting low frequency DFT coefficients of images and inverse transforming. ² By defining low-pass filters in spatial domain and obtaining filtered images by the convolution sum.