Periodicity
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u[n] and u(t) are the discrete and continuous unit step signals, respectively.
u[n] = \cases{1 &if \(\;n\ge 0\)\cr 0 &if \(\;n\lt 0\)\cr}\hskip4em
u(t) = \cases{1 &if \(\;t\gt 0\)\cr 1/2 &if \(\;t = 0\)\cr 0 &if \(\;t\lt 0\)\cr}
\delta[n] is the discrete unit sample signal.
\delta[n] = \cases{1 &if \(\;n = 0\)\cr 0 &otherwise\cr}
Part A
Determine whether or not each of the following signals is periodic.
4e^{j(t-\pi/4)}u(t)
u[n] + u[-n]
\sum_{k=-\infty}^{\infty}(\delta[n-8k] - \delta[n-2-8k]) for integer k
Part B
Determine whether or not each of the following signal is periodic. If a signal is not periodic, type "None". If a signal is periodic, specify its fundamental period. The constantse, pi, and j
have been defined for you.
a(t) = je^{j5t}\hskip2em
b(t) = e^{(j-1)t}\hskip2em
c[n] = e^{j5\pi n}\hskip2em
d(t) = 2e^{j3\pi(t+1/2)/5}\hskip2em
w[n] = 2e^{j3\pi(n+1/2)/5}\hskip2em
x(t) = 2e^{j\,3/5\,(t+1/2)}\hskip2em
y(t) = 2e^{j3\pi t/5\, + \,1/2}\hskip2em
z(t) = 2e^{(j3\pi\!/5 \,+ \,1/2)t}\hskip2em