12. What is the time-function v(t) if its Fourier transform is
V(j
ω
) ⫽0.5[cos2
ω
– jsin2
ω
]?
13. Find the Fourier transform of v(t) ⫽2e
–3|t|
.
14. Use the Fourier transform of a rectangular pulse to show that
(i) and (ii).
15. Find the Fourier transform of te
–
α
t
u(t) for a positive real
α
,
starting from the Fourier transform of e
–
α
t
u(t).
16. Verify the time-domain differentiation property of Fourier
transforms for v(t) ⫽e
–
α
t
u(t).
17. A signal v(t) has a normalised energy of 0.01 J. What is the
normalised energy of v(3t)?
18. If V
o
(j
ω
) ⫽10/(j
ω
⫹1) in the initially relaxed circuit in
Fig. 14.13-3, what is the v
i
(t) applied to it?
19. ...
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