GATE Electrical 2024 | Question: 28

Question

​​​Consider the discrete-time systems $T_{1}$ and $T_{2}$ defined as follows:
\[
\begin{array}{c}
\left\{T_{1} x\right\}[n]=x[0]+x[1]+\cdots+x[n] \\
\left\{T_{2} x\right\}[n]=x[0]+\frac{1}{2} x[1]+\cdots+\frac{1}{2^{n}} x[n]
\end{array}
\]

Which one of the following statements is true?

• A. $T_{1}$ and $T_{2}$ are BIBO stable.
• B. $T_{1}$ and $T_{2}$ are not BIBO stable.
• C. $T_{1}$ is BIBO stable but $T_{2}$ is not BIBO stable.
• D. $T_{1}$ is not BIBO stable but $T_{2}$ is BIBO stable.