How does the Discrete Fourier Transform relate to Spatial Domain Filtering?
The following convolution theorem shows an interesting relationship between the spatial domain and frequency domain: and, conversely, the symbol “*” indicates convolution of the two functions. The important thing to extract out of this is that the multiplication of two Fourier transforms corresponds to the convolution of the associated functions in the spatial domain. For instance, given a starting image of: We will apply a sobel filter to detect vertical edges.
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