Fundamental Periods

The questions below are due on Thursday September 11, 2025; 02:00:00 PM.

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Recall that the fundamental period of a periodic CT signal f(\cdot) is the smallest real value of T such that, for all t, f(t+T) = f(t).

Similarly, the fundamental period of a periodic DT signal f[\cdot] is the smallest integer value of N such that, for all n, f[n+N] = f[n].

For each function below what is its fundamental period? Enter each answer as a Python expression (and note that pi has been defined for you). If the given function is not periodic, enter None instead.

x_1(t) = \cos\left({10\pi\over 3}t + {\pi\over 4}\right)

T =~

x_2[n] = \cos\left({10\pi\over 3}n + {\pi\over 4}\right)

N =~

x_3(t) = 2\cos\left(10t + 1\right) - \sin\left(4t-1\right)

T =~

x_4[n] = \cos\left(0.6n\right)

N =~

x_5(t) = \cos\left({17\over 8}\pi t\right) + \sin\left({{\pi\over 2} t}\right) - \cos\left({5\over 6}\pi t\right)

T =~