What “fftshift” is used for?

What “fftshift” is used for? What will happen if ignore this step?

When a Fourier Transform is performed on a 1D signal, the DC element is placed at the first index of the Transform, followed by the next frequency bin in the spectrum and this proceeds that way [3]. The same is observed when Fourier Transform is performed on 2D signals (Images). For this to occur, the DC component is usually placed at the upper left corner of the initial index of the 2D matrix of Fourier Transform. Other frequency components which range from low to high are positioned relative to the DC component respectively. The results of a “Fourier Transform are displayed as asymmetrical frequency spectrum,” the other components, the DC component included, are positioned at the four corners of the frequency rectangle/spectrum [2].

The generated results are often 100% correct, however, the frequencies should be shifted from the corners to the center of the Frequency spectrum to achieve increased visibility and thus have a better analysis. The “fftshift” function in the image processing toolbox is used to carry out this process. Before this is done the frequencies usually appear increasingly from the corners to the center of the spectrum. The function “shift” simply reverses this and thus the frequencies increase from the center to the corner.

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The function of “fftshift” can be replaced by multiplying the input image by (-1)^(x+y) before computing FFT. Rewrite the program by this means and report if you get the same results.

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