Fourier transform for the function, Electrical Engineering

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The far-field pattern of an antenna can be modeled as the two dimensional Fourier Transform of the aperture.

1556_Bessel functions.png

1. Determine the 2D Fourier Transform for the function

240_Bessel functions1.png

This will require two transformations from rectangular coordinates, one in the spatial domain and one in the frequency domain. There are two key transformations. Explain.

Hint: This problem involves Bessel functions of the first kind of orders zero and one.

3) The figure illustrates a split circular cylinder of radius b and infinite length with equal and opposite potentials on the surfaces.

80_Bessel functions2.png

1.      Determine V(r,Φ) inside the tube.

2.      Provide a detailed discussion supporting your analysis of the boundary conditions


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