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State and prove the property of kernel separating and linearity for 2D-DFT.
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written 9.5 years ago by
teamques10
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1-Dimensional Fourier transform:
Let f(x) be a continuous function of x. The Fourier transform of f(x) is
$$F(u) =\int_{-∞}^∞ f(x) e^{-j2πux} dx \\ \hspace{3.4cm}=\int_{-∞}^∞ f(x)[cos2πux - j sin 2πux] dx$$
Similarly, the inverse fourier transform is
$$F(x)= \int_(-∞)^∞ f(x) e^{+j2πux} dx$$
Because f(u)is a complex
$$F(u)= R(u)+j I(u)$$
Where R …
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