For a unit step input \( u[n] \), a discrete-time LTI system produces an output signal \( \left( 2\delta[n + 1] + \delta[n] + \delta[n - 1] \right) \). Let \( y[n] \) be the output of the system for an input \( \left(\frac{1}{2}\right)^n u[n] \). The value of \( y[0] \) is _________.
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Top Questions on Convolution of Signals
- For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t) = x(t) * y(t)$ is maximum at $t = T_{1$. Then $T_{1}$ in seconds is \underline{\hspace{1cm}} (Round off to the nearest integer).} \begin{center} \includegraphics[width=0.5\textwidth]{13.jpeg} \end{center}
- GATE EE - 2023
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- Convolution of Signals
- Consider two 16-point sequences \(x[n]\) and \(h[n]\). Let the linear convolution of \(x[n]\) and \(h[n]\) be denoted by \(y[n]\), while \(z[n]\) denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of \(x[n]\) and \(h[n]\). The value(s) of \(k\) for which \(z[k] = y[k]\) is/are
- GATE EC - 2021
- Signals and Systems
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- Consider the function \( f: \mathbb{R} \to \mathbb{R} \), defined as \[ f(x) = 2x^3 - 3x^2 - 12x + 1. \] Which of the following statements is/are correct? (Here, \( \mathbb{R} \) is the set of real numbers.)
- GATE EC - 2025
- Calculus
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable \( X \) denote the sum of the outcomes obtained. The expectation of \( X \) is _________ (rounded off to two decimal places).
- GATE EC - 2025
- Simple diode circuits
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is: