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In image processing, a Guassian filter is used to blur an image. A low-pass filter is a filter that attenuates the high frequencies, preserving only smooth variations in the provided image. Is a Guassian filter a low-pass filter because it smooths the edges (or, in general, the parts of the image where there is a high variation of the intensity)? Why exactly is the Guassian filter a low-pass filter?

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Because the Fourier transform of Gaussian in the spatial/temporal domain is also a Gaussian in the frequency domain. Since a Gaussian drops off rapidly with frequency, it's a low pass filter.

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