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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