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A relaxed linear time-invariant system with impulse response \[ h(n)=a^n u(n), \qquad |a|<1 \] when the input is a unit step sequence, \[ x(n)=u(n), \] then the output \(y(\infty)\) of the system is

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For \[ \sum_{k=0}^{n}r^k = \frac{1-r^{n+1}}{1-r}. \] Always recognize geometric series immediately in DSP problems.

Updated On: Jun 25, 2026

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A periodic signal \(x(t)\) of period \(T_0\) is given by \( x(t) = \begin{cases} 1, & |t|<T_1 \\ 0, & T_1<|t|<\frac{T_0}{2} \end{cases} \). The dc component of \(x(t)\) is
- CUET (PG) - 2025
- Electronics Engineering
- Signals and Systems
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Signals and their Fourier Transforms are given in the table below. Match LIST-I with LIST-II and choose the correct answer.

LIST-I	LIST-II
A. \( e^{-at}u(t), a>0 \)	I. \( \pi[\delta(\omega - \omega_0) + \delta(\omega + \omega_0)] \)
B. \( \cos \omega_0 t \)	II. \( \frac{1}{j\omega + a} \)
C. \( \sin \omega_0 t \)	III. \( \frac{1}{(j\omega + a)^2} \)
D. \( te^{-at}u(t), a>0 \)	IV. \( -j\pi[\delta(\omega - \omega_0) - \delta(\omega + \omega_0)] \)