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I was trying to understand the 2d dft(discrete Fourier transform) and discrete spatial Fourier transform (dsft) of images.

But while understanding the graph i didn't understand that how come ($\pi,\pi$) is high frequency component and not ($2\pi,2\pi$) is the highest frequency component.graph of the H(w1,w2)

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Note that the terms $e^{j\omega_in_i}$ in the formula of the Fourier transform are $2\pi$-periodic. Consequently, the Fourier transform $H(\omega_1,\omega_2)$ is also periodic in both dimensions with period $2\pi$. If we choose $\omega=0$ as the center of our fundamental interval (as shown in the figure), the fundamental interval extends from $-\pi$ to $\pi$. The frequency $\omega=\pi$ is referred to as the Nyquist frequency, and it corresponds to the maximum possible frequency of a discrete signal.

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