Home/Engineering & CS/Determine the period of each of the following discrete-time or continuous-time signals. If a signal is not periodic, mention its period as infinity. As before, \( n \) is the discrete-time variable and \( t \) is the continuous-time variable. (25 points) a) \( \cos (2 \pi 0.15 n) \) b) \( \sin (\pi 0.12 n+\pi / 4) \) c) \( e^{j \cos (\pi 0.12 n)} \) d) \( \cos (2 \pi 0.35 n+\pi / 100)+4 \sin (2 \pi 0.25 n) \) e) \( x(t)=\sum_{i=-\infty}^{\infty} p(t-3 i) \) where \( p(t) \) is any waveform of finite duration. Hint: sketch and observe \( x(t) \) by assuming a narrow pulse \( p(t) \) and then prove your finding if you can.

Question Solved1 Answer Determine the period of each of the following discrete-time or continuous-time signals. If a signal is not periodic, mention its period as infinity. As before, \( n \) is the discrete-time variable and \( t \) is the continuous-time variable. (25 points) a) \( \cos (2 \pi 0.15 n) \) b) \( \sin (\pi 0.12 n+\pi / 4) \) c) \( e^{j \cos (\pi 0.12 n)} \) d) \( \cos (2 \pi 0.35 n+\pi / 100)+4 \sin (2 \pi 0.25 n) \) e) \( x(t)=\sum_{i=-\infty}^{\infty} p(t-3 i) \) where \( p(t) \) is any waveform of finite duration. Hint: sketch and observe \( x(t) \) by assuming a narrow pulse \( p(t) \) and then prove your finding if you can.

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Transcribed Image Text: Determine the period of each of the following discrete-time or continuous-time signals. If a signal is not periodic, mention its period as infinity. As before, \( n \) is the discrete-time variable and \( t \) is the continuous-time variable. (25 points) a) \( \cos (2 \pi 0.15 n) \) b) \( \sin (\pi 0.12 n+\pi / 4) \) c) \( e^{j \cos (\pi 0.12 n)} \) d) \( \cos (2 \pi 0.35 n+\pi / 100)+4 \sin (2 \pi 0.25 n) \) e) \( x(t)=\sum_{i=-\infty}^{\infty} p(t-3 i) \) where \( p(t) \) is any waveform of finite duration. Hint: sketch and observe \( x(t) \) by assuming a narrow pulse \( p(t) \) and then prove your finding if you can.
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Transcribed Image Text: Determine the period of each of the following discrete-time or continuous-time signals. If a signal is not periodic, mention its period as infinity. As before, \( n \) is the discrete-time variable and \( t \) is the continuous-time variable. (25 points) a) \( \cos (2 \pi 0.15 n) \) b) \( \sin (\pi 0.12 n+\pi / 4) \) c) \( e^{j \cos (\pi 0.12 n)} \) d) \( \cos (2 \pi 0.35 n+\pi / 100)+4 \sin (2 \pi 0.25 n) \) e) \( x(t)=\sum_{i=-\infty}^{\infty} p(t-3 i) \) where \( p(t) \) is any waveform of finite duration. Hint: sketch and observe \( x(t) \) by assuming a narrow pulse \( p(t) \) and then prove your finding if you can.
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