Consider the following signals: (i) xa(t) = 2 [cos (2πt) + cos (8t)]² Xb )=sin (4.8 7t+ ) + cos (43.2 + ) +) mt 3 By considering the fundamental frequencies of the signals xa(t) and (t), determine if they are periodic or non-periodic. Carefully justify your answer.

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i)

Consider the following signals:
(i)
(ii)
(iii)
(iv)
Ta(t) = 2 [cos (2πt) + cos (8t)]²
ㅠ
ㅠ
-5) +cos (43.2 πt +
xi(t) = sin (4.8 nt+
By considering the fundamental frequencies of the signals xa(t) and
(t), determine if they are periodic or non-periodic. Carefully justify
your answer.
For the signal in part e) (i) that is periodic, write down its fundamental
frequency in hertz.
For the signal in part e) (i) that is periodic, write down the
trigonomentric Fourier series representation without performing any
integration.
For the non-periodic signal in part e) (i), sketch the spectrum of the
resulting signal when the non-periodic signal is sampled at 40 rad/s,
carefully labelling all the frequency components present in the signal
and their amplitudes.
Transcribed Image Text:Consider the following signals: (i) (ii) (iii) (iv) Ta(t) = 2 [cos (2πt) + cos (8t)]² ㅠ ㅠ -5) +cos (43.2 πt + xi(t) = sin (4.8 nt+ By considering the fundamental frequencies of the signals xa(t) and (t), determine if they are periodic or non-periodic. Carefully justify your answer. For the signal in part e) (i) that is periodic, write down its fundamental frequency in hertz. For the signal in part e) (i) that is periodic, write down the trigonomentric Fourier series representation without performing any integration. For the non-periodic signal in part e) (i), sketch the spectrum of the resulting signal when the non-periodic signal is sampled at 40 rad/s, carefully labelling all the frequency components present in the signal and their amplitudes.
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