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Unformatted text preview: Uniﬁed Engineering II Spring 2004 Problem S15 (Signals and Systems)
Find the Fourier transforms of the following signals:
g (t) = δ (t − T )
Note: The system with impulse response g (t) produces an output that is the
input delayed by T . Since delays occur frequently in signal processing, G(jω ) is
an important transfer function.
1, |t| ≤ T
g (t) =
0, |t| > T
Note: Because g (t) is symmetric, G(jω ) should be real. Please express your
answer so that it is apparent that the answer is real. 3. 1
Hint: If you ﬁnd the integral hard to do, you might be able to ﬁnd the answer
g (t) = 4.
g (t) = t2 sin π t/T
π t/T Hint: You almost certainly won’t be able to do the FT integral directly. Use
duality and the results of (2) above to ﬁnd the answer. The g (t) in this problem
has important connections to, among other things, CD players!
5. Find the inverse transform of
G(jω ) = sin ω T
ωT �2 using the results of part (2), and FT properties. ...
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- Fall '05