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

For each of the following systems, determine whether or not the system is Time-Invariant, Linear, and causal.

a.) y[n] = x[n]cos(0.2*pi*n)

there are more but if I can figure this out I should be able to get the others

2. Relevant equations

Time Invariant ---> if x[n] produces y[n] then x[n - d] produces y[n - d]

Linear ---> if x1[n] produces y1[n] and x2[n] produces y2[n], then x[n] = ax1[n] + bx2[n] produces y[n]=ay1[n] + by2[n]

3. The attempt at a solution

I am able to prove that y[n] = x[n]cos(0.2*pi*n) is linear by saying

let x[n] = ax1[n] + bx2[n]

then y[n] = (ax1[n] + bx2[n])cos(0.2*pi*n) = ax1[n]cos(0.2*pi*n) + bx2[n]cos(0.2*pi*n)

so y[n] = ay1[n] + by2[n] proving that it is linear

I am not able to prove, at this point, that y[n] is either time-invariant or not.

All I have is this:

let g[n] = x[n - d]

then y[n - d] = g[n]cos(0.2*pi*n) = x[n - d]cos(0.2*pi*n), so it is time-invariant?

This doesn't seem right though for whatever reason.

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# Homework Help: Determining if a System is Time-Invariant and/or Linear

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