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The question is this:
$$ y[n] = \cos\left(\frac{5\pi}{8}n + \frac{\pi}{4}\right)$$
This is what my teacher said when I asked him for help-:
In any system, inputs are not given, then we have to assume input is impulse signal. Then the response is impulse response
I really couldn't comprehend much of what he said, but I still tried my best, and this is what I got:
Am I correct? (I Don't Think so as I believe this should be a non linear system, I have a gut feeling).
Can you help me here?
$y[n] = \cos(\frac{5\pi}{8}n + \frac{\pi}{4})$ is not a system, but a signal.
Anyway, if you insist that you have a system with a fixed output $y[n] = \cos(\frac{5\pi}{8}n + \frac{\pi}{4})$, then this will be a non-linear system.
Proof is easy: assume an arbitrary input $x_1[n]$ to your system. The output will be $y_1[n] = \cos(\frac{5\pi}{8}n + \frac{\pi}{4})$. Then, assume another input $x_2[n] = a ~ x_1[n]$ , the output will be $y_2[n] = \cos(\frac{5\pi}{8}n + \frac{\pi}{4})$. Then since $y_2[n] \neq a ~y_1[n]$, the system cannot be linear; thus it must be nonlinear.
