(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is the following system linear:

[tex] y(n) = x(n) + 0.8y(n-1) [/tex]

3. The attempt at a solution

I'm really stuck on this one.

My idea was to assume that the system is casual, find the impulse response and then use the fact that: [tex] y(n)=x(n)*h(n) [/tex]. However, if I assume that the output is the convolution of the impulse response and the input, I have ALREADY ASSUMED (and not proven) that the system is linear.

So I am lost.

I can't wrap my brain around the fact that the output depends on the input and the previous output.

Another idea I had is that if I show that I input a sinusoid and I get a scaled and phase shifted sinusoid, then the system is LTI.

Any help?

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# Homework Help: Show that the system is linear?

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