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fft2 2-D fast Fourier transformcollapse all in page Syntax Y = fft2(X) Y = fft2(X,m,n) Description example Y = fft2(X) returns the two-dimensional Fourier transform of a matrix using a fast Fourier transform algorithm, which is equivalent to computing fft(fft(X).').'. If X is a multidimensional array, then fft2 takes the 2-D transform of each dimension higher than 2. The output Y is the same size as X. example Y = fft2(X,m,n) truncates X or pads X with trailing zeros to form an m-by-n matrix before computing the transform. Y is m-by-n. If X is a multidimensional array, then fft2 shapes the first two dimensions of X according to m and n. Examples collapse all 2-D Transform View MATLAB Command The 2-D Fourier transform is useful for processing 2-D signals and other 2-D data such as images. Create and plot 2-D data with repeated blocks. P = peaks(20); X = repmat(P,[5 10]); imagesc(X) Figure contains an axes. The axes contains an object of type image. Compute the 2-D Fourier transform of the data. Shift the zero-frequency component to the center of the output, and plot the resulting 100-by-200 matrix, which is the same size as X. Y = fft2(X); imagesc(abs(fftshift(Y))) Figure contains an axes. The axes contains an object of type image. Pad X with zeros to compute a 128-by-256 transform. Y = fft2(X,2^nextpow2(100),2^nextpow2(200)); imagesc(abs(fftshift(Y))); Figure contains an axes. The axes contains an object of type image. Input Arguments collapse all X — Input array matrix | multidimensional array Input array, specified as a matrix or a multidimensional array. If X is of type single, then fft2 natively computes in single precision, and Y is also of type single. Otherwise, Y is returned as type double. Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical Complex Number Support: Yes m — Number of transform rows positive integer scalar Number of transform rows, specified as a positive integer scalar. Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical n — Number of transform columns positive integer scalar Number of transform columns, specified as a positive integer scalar. Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical More About collapse all 2-D Fourier Transform This formula defines the discrete Fourier transform Y of an m-by-n matrix X: Y p+1,q+1 = m−1 j=0 n−1 k=0 ω jp m ω kq n X j+1,k+1 ωm and ωn are complex roots of unity: ω m =e −2πi/m ω n =e −2πi/n i is the imaginary unit. p and j are indices that run from 0 to m–1, and q and k are indices that run from 0 to n–1. This formula shifts the indices for X and Y by 1 to reflect matrix indices in MATLAB®. |
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