Question

Suppose that a continuous-time sinusoid x(t) is sampled at a rate of 500 samples/sec, resulting in the following discrete-time signal: $x[n] = 8 \cos \left(\frac{4\pi}{5}n + \frac{\pi}{6}\right)$ Knowing x[n] does not uniquely determine x(t); there are many continuous-time sinusoidal signals x(t) that when sampled would produce this x[n]. Name three that have a frequency less than 800 Hz. In other words, specify three different continuous-time sinusoidal signals $x_1(t) = A_1 \cos(2\pi f_1 t + \phi_1)$, $x_2(t) = A_2 \cos(2\pi f_2 t + \phi_2)$, and $x_3(t) = A_3 \cos(2\pi f_3 t + \phi_3)$ that could have produced this particular x[n], subject to the constraint that $0 < f_i < 800$ Hz in all cases.

          Suppose that a continuous-time sinusoid x(t) is sampled at a rate of 500 samples/sec, resulting in the following discrete-time signal:
$x[n] = 8 \cos \left(\frac{4\pi}{5}n + \frac{\pi}{6}\right)$
Knowing x[n] does not uniquely determine x(t); there are many continuous-time sinusoidal signals x(t) that when sampled would produce this x[n]. Name three that have a frequency less than 800 Hz. In other words, specify three different continuous-time sinusoidal signals $x_1(t) = A_1 \cos(2\pi f_1 t + \phi_1)$, $x_2(t) = A_2 \cos(2\pi f_2 t + \phi_2)$, and $x_3(t) = A_3 \cos(2\pi f_3 t + \phi_3)$ that could have produced this particular x[n], subject to the constraint that $0 < f_i < 800$ Hz in all cases.

Suppose that a continuous-time sinusoid x(t) is sampled at a rate of 500 samples/sec, resulting in the following discrete-time signal:
x[n] = 8 cos((4π)/(5)n + (π)/(6))
Knowing x[n] does not uniquely determine x(t); there are many continuous-time sinusoidal signals x(t) that when sampled would produce this x[n]. Name three that have a frequency less than 800 Hz. In other words, specify three different continuous-time sinusoidal signals x1(t) = A1 cos(2π f1 t + ϕ1), x2(t) = A2 cos(2π f2 t + ϕ2), and x3(t) = A3 cos(2π f3 t + ϕ3) that could have produced this particular x[n], subject to the constraint that 0 < fi < 800 Hz in all cases.

Added by Randall G.

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