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Determine whether the following systems are causal or non-causal.$$y(n)=x(n)+\frac{1}{x(n-1)} $$
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Solution:

Given: output of the system $y(n)=x(n)+\frac{1}{x(n-1)}$

For $\mathrm{n}=-1 ; \quad y(-1)=x(-1)+\frac{1}{x(-2)}$

For $\mathrm{n}=0 ; \quad y(0)=x(0)+\frac{1}{x(-1)}$

For $\mathrm{n}=1 ; \quad y(1)=x(1)+\frac{1}{x(0)}$

For all values of ā€˜nā€™, the output depends on present and past inputs. Therefore, the system is causal.

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