1.

Determine the output y(n) of a LTI system with impulse response h(n)=a^nu(n), |a|

Answer»

Correct option is (a) \(\frac{1-a^{N+1}}{1-a}\)

Easiest explanation: Now fold the signal x(n) and shift it by ONE UNIT at a time and SUM as follows

y(0)=x(0)h(0)=1

y(1)=h(0)x(1)+h(1)x(0)=1.1+a.1=1+a

y(2)=h(0)x(2)+h(1)x(1)+h(2)x(0)=1.1+a.1+a^2.1=1+a+a^2

Similarly, y(n)=1+a+a^2+….a^n=\(\frac{1-a^{n+1}}{1-a}\).



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