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6. Properties of 2D Fourier transforms Given a function f(x,y) and its 2-D Fourier transform F(u, v): (a) Derive the effect on F of a general linear transformation, x Ax, where x = (x, y) and A is a 2D linear transformation matrix. (b) Suppose the function f(x,y) has rotational symmetry so that f(x, y) = f(r) where r2 = 2 + y2 Show that its Fourier transform is also rotationally symmetric. 6. Properties of 2D Fourier transforms Given a function f(x,y) and its 2-D Fourier transform F(u, v): (a) Derive the effect on F of a general linear transformation, x Ax, where x = (x, y) and A is a 2D linear transformation matrix. (b) Suppose the function f(x,y) has rotational symmetry so that f(x, y) = f(r) where r2 = 2 + y2 Show that its Fourier transform is also rotationally symmetric