Question:
The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system \( \mathcal{S} \). The output is observed to be the continuous-time unit step signal \( u(t) \). Which one of the following statements is true?
The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system \( \mathcal{S} \). The output is observed to be the continuous-time unit step signal \( u(t) \). Which one of the following statements is true?
Show Hint
A system is BIBO stable only if its impulse response is absolutely integrable. If \( h(t) = u(t) \), the system is not BIBO stable.
Updated On: Feb 3, 2026
Every bounded input signal applied to S results in a bounded output signal.
t is possible to find a bounded input signal which when applied to S results in an unbounded output signal.
On applying any input signal to S, the output signal is always bounded.
On applying any input signal to S, the output signal is always unbounded.
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The impulse response \( h(t) \) of the system \( \mathcal{S} \) is the output observed when the input is a Dirac delta \( \delta(t) \).
Given:
\[
h(t) = u(t)
\]
Now consider the bounded-input bounded-output (BIBO) stability condition:
A system is BIBO stable if and only if its impulse response is absolutely integrable:
\[
\int_{-\infty}^{\infty} |h(t)| \, dt<\infty
\]
But for \( h(t) = u(t) \), we have:
\[
\int_{0}^{\infty} 1 \, dt = \infty
\]
So the system is not BIBO stable. Hence, there exists at least one bounded input signal that can lead to an unbounded output signal.
Was this answer helpful?
0
0
Top GATE EE Signals and Systems Questions
- Consider a vector \( \Bar{u} = 2\hat{x} + \hat{y} + 2\hat{z} \), where \( \hat{x}, \hat{y}, \hat{z} \) represent unit vectors along the coordinate axes \( x, y, z \) respectively. The directional derivative of the function \( f(x, y, z) = 2 \ln(xy) + \ln(yz) + 3 \ln(xz) \) at the point \( (x, y, z) = (1, 1, 1) \) in the direction of \( \mathbf{u} \) is:
- The input \( x(t) \) and the output \( y(t) \) of a system are related as \[ y(t) = e^{-t} \int_{-\infty}^t e^t x(\tau) d\tau, \quad -\inftyLt;tLt;\infty. \] The system is:
Consider the discrete-time systems $ T_1 $ and $ T_2 $ defined as follows:
$ [T_1x][n] = x[0] + x[1] + \dots + x[n], $
$ [T_2x][n] = x[0] + \frac{1}{2}x[1] + \dots + \frac{1}{2^n}x[n]. $
Which of the following statements is true?- If the Z-transform of a finite-duration discrete-time signal \( x[n] \) is \( X(z) \), then the Z-transform of the signal \( y[n] = x[2n] \) is:
- For the block diagram shown in the figure, the transfer function \(\dfrac{Y(s)}{R(s)}\) is: \begin{center} \includegraphics[width=0.5\textwidth]{04.jpeg} \end{center}
View More Questions
Top GATE EE Questions
- If ‘→’ denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [please → \_\_\_\_\_ → pander]. Which one of the given options is appropriate to fill the blank?
- \(P\) and \(Q\) have been allotted a hostel room with two beds, a study table, and an almirah. \(P\) is an avid birdwatcher and wants to sit at the table and watch birds outside the window. \(Q\) prefers a bed close to the ceiling fan. Which one of the following arrangements suits them the most?
- The decimal number system uses the characters \(0, 1, 2, ..., 8, 9,\) and the octal number system uses the characters \(0, 1, 2, ..., 6, 7.\) For example, the decimal number \(12 (= 1 \times 10^1 + 2 \times 10^0)\) is expressed as \(14 (= 1 \times 8^1 + 4 \times 8^0)\) in the octal number system. The decimal number 108 in the octal number system is:
- A shopkeeper buys shirts from a producer and sells them at 20\% profit. A customer has to pays Rs. 3186 including 18\% taxes per shirt. At what price did the shopkeeper buy each shirt?
- If, for non-zero real variables \(x, y\) and a real parameter \(a>1\), \(x : y = (a+1) : (a-1)\). Then, the ratio \((x^2 - y^2) : (x^2 + y^2)\) is:
View More Questions