railway RRB JE (CBT I + CBT II) Mock Test 2024 Signals and Systems Discrete Time Signals and Systems
Consider the system with impulse response h(n) = an u(n), 0 < a < 1. Let u(n) denote the discrete time unit step signal. Given that signal x(n) = u(n) - u(n - N) is applied as input to the above system. The output of the system for n ≥ 0, is
1
\(\left\{ {\begin{array}{*{20}{l}} {{a^{n - N + 1}}\left( {\frac{{1 - {a^N}}}{{1 - a}}} \right)for{\rm{\;}}0 \le n \le N - 1}\\ {\frac{{1 - {a^{n + 1}}}}{{1 - a}}{\rm{\;}}for{\rm{\;}}n \ge N} \end{array}} \right.\)
2
\({a^{n - N + 1}}\left( {\frac{{1 - {a^N}}}{{1 - a}}} \right){\rm{\;}}for{\rm{\;}}all{\rm{\;}}n\)
3
\(\left\{ {\begin{array}{*{20}{c}} {\frac{{1 - {a^{n + 1}}}}{{1 - a}}{\rm{\;}}for{\rm{\;}}0 \le n \le N - 1}\\ {{a^{n - N + 1}}\left( {\frac{{1 - {a^N}}}{{1 - a}}} \right){\rm{\;}}for{\rm{\;}}n \ge N} \end{array}} \right.\)
4
\(\frac{{1 - {a^{n + 1}}}}{{1 - a}}for{\rm{\;}}all{\rm{\;}}n\)