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1

Your intuition that you need initial conditions to fully solve this is correct, so it becomes a problem in test-taking. Were it me, and were the test proctored by the prof, then I would go to the front of the room and ask. Failing that, I would first solve for $y[10]$ in terms of $y[0]$, $y[1]$ and $y[2]$, then I would point out that as they were not given, ...

0

You're right that the question cannot be answered as stated, and there is no "right approach". There are infinitely many solutions of the given difference equation, so without any further assumptions there is no way to compute $y[10]$, or any other value for that matter. Let $p_1$ and $p_2$ be the two distinct solutions of the characteristic ...

3

I'm not gonna give you a complete answer but I can help you. Your open-loop transfer function has 2 poles at $-1 ±j \sqrt(3)$ Good news, they are stable. However, they are not damped and they are slow. Your strategy is this 1 - Damp the poles, this will reduce the overshoot. 2 - Try to increase the poles frequency. This will reduce the settling time. 3 - ...

1

The Nyquist criterion states that the sampling frequency should be minimum twice the signal frequency. In this case it should be 50 kHz. A more precise statement is that the sampling frequency should more than twice the bandwidth. Usually, you want a bandwidth that include zero frequency, making the bandwidth and the maximum frequency the same, but that is ...

21

As correctly stated in Peter K.'s answer, this question is about aliasing. Since you can't sample at a rate that is sufficiently high to avoid aliasing - i.e., $f_s>50\textrm{ kHz}$ - you have to take aliasing into account. Now it's your task to figure out the aliased frequencies of the given signals for the different sampling rates. If you understand how ...

29

HINT When you sample at below the Nyquist rate, aliasing happens. That means frequencies higher than half the sampling rate get folded back down to below half the sampling rate. Have a read about bandpass sampling. PS: Tell your teacher, that's a really nice question. :-)

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