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Linearity and Time Invariance

For the system

Xk[n]=d[n-k]

The output is defined as

Yk[n]=(k+1)2 d[n-(k+1)]

a) Time Invariance

This system is not time invariant because it is dependent on the time shift $ k $. If the time is shifted before being put through the system, there will be a different output than if it is put through the system and then time shifted.

b) Looking at the examples on Mimi's homework page[[1]], the x[n] to produce the output Y[n]=u[n-1] would be u[n].

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Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

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