Added filtering example

filtering/README.md

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+# Filtering
+
+## Topic
+
+Applying linear filters to an image in the spatial domain and in the frequency
+domain
+
+## Aim
+
+Implement an algorithm for linear filtering of an image in the frequency domain,
+set the transfer function of a low-frequency filter with the specified properties,
+find the appropriate filter mask in the spatial domain and apply it, compare the
+results of applying filters to the image in the frequency and spatial domain.
+
+## Instructions:
+
+1. Upload a color image (dog.jpg), find its spectrum by applying a two-dimensional
+discrete Fourier transform (DFT), show the image and its spectrum on the screen
+2. Set the transfer function of the low-pass Gaussian filter for the cutoff frequency
+of 0.1 1/pixel, show a graph of the transfer function (the abscissa axis should be graded to 1/pixel),
+mark the cutoff frequency on the graph
+3. Apply the transfer function to the image spectrum, show the image spectrum after
+filtering, find the inverse DFT, show the resulting image
+4. Calculate the inverse DFT of the transfer function, get a filter mask in the spatial
+domain and crop it to size 11×11 so that the mask is symmetrical with respect
+to the central element, show a graph of the resulting filter mask
+5. Perform convolution of the image with the filter mask in the spatial area, using
+the addition of zeros at the edges of the image, show the result of filtering on the screen
+6. Compare the results obtained in paragraphs 3 and 5, visually, show those areas of the image where
+the results are noticeably different, explain the reason for the difference and how the result will change if
+you use a periodic continuation of the image along the edges when performing convolution in
+the spatial domain
+7. Make a conclusion about the correspondence of the use of a linear filter in the spatial and frequency
+domain.