H is a discrete-time LTI system with impulse response h[n] = δ[n] − 2δ[n − 1] + 3δ[n − 2]. Find the output signal y[n] in terms of the input signal x[n] (use the convolution equation and the properties of convolution with deltas). Hint: since the input signal x[n] is unknown, your answer should express the output signal y[n] as a linear combination of the shifts of x[n].

The output is given as

Step-by-step explanation:

As the output is given as y(n) and the input is given as x(n) thus the

equation of the output is given as

Here the impulse response h(n) is given as

So the output is given as

By distributive property,

Now by the convolution properties with delta

so

So the output is given as

answer for #1 is c

answer for #2 is d

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