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P21400_EX2_2020-21
(a) if $x(t) = e^{-2t}u(t)$, determine, using tables, the Fourier transform of the function
y(t) = x(t - 5)
[5 Marks]
(b) Using tables, determine the Fourier transform of the function
x(t) = $e^{-4t}u(-t)$
[5 Marks]
(c) Using tables, find the time function, x(t), whose Fourier transform is
$X(\omega) = 3 + 8\delta(\omega) + 2e^{-j\omega}$
[5 Marks]
(d) The two functions, $f_1(t)$ and $f_2(t)$, shown both graphically and analytically in Fig. 1d, are
two instances of horizontal (time) zooming on a scope.
$f_1(t)$
$f_2(t)$
$f_1(t) = \frac{1}{1 + (3t)^2}$
$f_2(t) = \frac{1}{1 + e^t}$
Fig. 1d
Using tables, find
(i) the Fourier transform of $f_1(t)$ (applying duality)
[7 Marks]
(ii) the Fourier transform of $f_2(t)$
[3 Marks]
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