Question:
Show Hint
The output of an LTI system is the convolution of the input with the system’s impulse response. When \( h[n] \) is nonzero for \( n = 0,1,2 \), the output becomes a weighted sum of the current and two past input values.
Updated On: Feb 3, 2026
- \( x[n] + x[n-1] + x[n-2] \)
- \( x[n-1] + x[n] + x[n+1] \)
- \( x[n] + x[n+1] + x[n+2] \)
- \( x[n+1] + x[n+2] + x[n+3] \)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The system's impulse response \( h[n] = \mathcal{S}\{\delta[n]\} \) is:
\[
h[n] =
\begin{cases}
1, & n = 0, 1, 2 \\
0, & \text{otherwise}
\end{cases}
\]
This means the system performs convolution:
\[
y[n] = x[n] * h[n] = \sum_{k=-\infty}^{\infty} x[k] h[n - k]
\]
Since \( h[n] = \delta[n] + \delta[n-1] + \delta[n-2] \), we get:
\[
y[n] = x[n] + x[n-1] + x[n-2]
\]
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