Show that the 2-D Fourier transform of the rect function is the sinc function, whereas the 2-D…

Show that the 2-D Fourier transform of the rect function is
the sinc function, whereas the 2-D Fourier transform of the sinc function is
the rect function. Determine the values of E_ and P_ for the sinc function
(see Problem 2.3).

Problem 2.3

We define the energy of a signal f in the finite rectangular
window defined by _X _ x _ X and _Y _ y _
Y, where X,Y < _,="" & Show that the 2-D Fourier transform of the rect function is the sinc function, whereas the 2-D Fourier transform of the sinc function is the rect function. Determine the values of E_ and P_ for the sinc function (see Problem 2.3). Problem 2.3 We define the energy of a signal f in the finite rectangular window defined by _X _ x _ X and _Y _ y _ Y, where X,Y < _,="" where f might be complex-valued, in which case || denotes complex magnitude (or modulus). The total energy is defined as The power of signal f is defined as and the total power as For each of the signals in Problem 2.1, determine the values of E_ and P_.

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