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Two-Dimensional Discrete Fourier Transform is a digital transformation method that is generally used to transform an image from the spatial domain to the frequency domain. It is used for image enhancement, image denoising, image edge detection, and image feature extraction. , Image compression and other applications all play an extremely important role.

Two-dimensional discrete Fourier transform

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Two-Dimensional Discrete Fourier Transform is a digital transformation method that is generally used to transform an image from the spatial domain to the frequency domain. It is used for image enhancement, image denoising, image edge detection, and image feature extraction. , Image compression and other applications all play an extremely important role.
Chinese name
Two-dimensional discrete Fourier transform
Foreign name
2D-DFT; Two-Dimensional Discrete Fourier Transform
Origin
Fourier transform; discrete Fourier transform
Application
2D image processing
Two-dimensional discrete Fourier transform is a transform method that transforms an image from the spatial domain to the frequency domain. An image is essentially a two-dimensional number table or matrix. Converting the image in the spatial domain (two-dimensional gray number table) to the frequency domain (frequency number table) can more intuitively observe and process the image, and it is more conducive to operations such as frequency domain filtering. The formula of the two-dimensional discrete Fourier transform is shown in the figure. Where f (x, y) represents a matrix of size M x N, where x = 0,1,2, ..., M-1 and y = 0,1,2, ..., N- 1, F (u, v) represents the Fourier transform of f (x, y). Can be converted to a trigonometric representation where u and v can be used to determine the frequency of the sine and cosine. The coordinate system where F (u, v) is called the frequency domain, M defined by u = 0,1,2, ..., M-1 and v = 0,1,2, ..., N-1 The x N matrix is often called the frequency domain matrix. The coordinate system where f (x, y) is called the space domain is defined by x = 0,1,2, ..., M-1 and y = 0,1,2, ..., N-1 M x N matrices are often called spatial domain matrices. Obviously, the size of the frequency domain matrix is the same as that of the original space domain matrix. Each point in the frequency domain matrix represents a function with frequencies u, v. The combination of these functions in the spatial domain is the original function f (x, y).
Accordingly, the two-dimensional discrete inverse Fourier transform transforms the number table in the frequency domain into a two-dimensional number table in the spatial domain.
Two-dimensional discrete Fourier transform

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