The system is defiantly not time invariant. When the signal is shifted the output is shifted also but a different magnitude is applied to the output, showing that time affects the output.


Sine we are talking about DT a setup of

$ X[n]=\sum_{k=-\infty}^{\infty} $ δ[n-k].

However for $ u[n] $ we will need to cap off the $ -\infty $ to 0, since the for all values less then 0 the unit step would produce 0.

X[n]=$ \sum_{k=0}^{\infty} $ δ[n-k].

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

Buyue Zhang