Sketch the periodic signal k(t) = E- m(t + cT) where the period T = 3s for a given signal m(t) in Figure 06(a). Proof that by using the exponential Fourier Series, the signal expansion of k(t) is given by the following expression: (Hint: Simplify the coefficient x, in term of sinc function) Q6 (a) () k(t) == a-2), sinc (i) Based on the answer in 06(a}i), predict the amplitude spectrum of the non- periodic signal m(t) in Figure Q6(a) with T = 200 s. (b) Based on your understanding, give a suggestion to calculate the frequency domain of signal x(t) = e"u(t) and state your justification. m(t) 1 T Figure Q6(a)

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Sketch the periodic signal k(t) = E-o m(t + cT) where the period T = 3 s
for a given signal m(e) in Figure 06(a). Proof that by using the exponential
Fourier Series, the signal expansion of k(t) is given by the following
expression: (Hint: Simplify the coefficient x, in term of sinc function)
Q6
(a)
(i)
00
k(t) =
-20) sinc
n=-00
(ii)
Based on the answer in 06(a)(i), predict the amplitude spectrum of the non-
periodic signal m(t) in Figure O6(a) with T = 200 s.
(b) Based on your understanding, give a suggestion to calculate the frequency domain of
signal x(t) = et u(t) and state your justification.
m(t)
1
t
1
T
Figure Q6(a)
Transcribed Image Text:Sketch the periodic signal k(t) = E-o m(t + cT) where the period T = 3 s for a given signal m(e) in Figure 06(a). Proof that by using the exponential Fourier Series, the signal expansion of k(t) is given by the following expression: (Hint: Simplify the coefficient x, in term of sinc function) Q6 (a) (i) 00 k(t) = -20) sinc n=-00 (ii) Based on the answer in 06(a)(i), predict the amplitude spectrum of the non- periodic signal m(t) in Figure O6(a) with T = 200 s. (b) Based on your understanding, give a suggestion to calculate the frequency domain of signal x(t) = et u(t) and state your justification. m(t) 1 t 1 T Figure Q6(a)
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