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GATE ECE 2020 | Question: 52
$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (rounded off to two decimal places) is ____________

go_editor asked in Continuous-time Signals Feb 13, 2020

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GATE ECE 2019 | Question: 28
Consider a six-point decimation-in-time Fast Fourier Transform $(FFT)$ algorithm, for which the signal-flow graph corresponding to $X[1]$ is shown in the figure. Let $W_{6}=exp\left(-\:\dfrac{j2\pi}{6}\right).$ In the figure, what should be the values of the coefficients $a_{1},a_{2},a_{3}$ ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$

Arjun asked in Continuous-time Signals Feb 12, 2019

by Arjun

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GATE ECE 2016 Set 1 | Question: 35
Consider the signal $x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]$ If $X(e^{jw})$ is the discrete-time Fourier transform of $x[n]$, then $\frac{1}{\pi} \int\limits_{-\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega$ is equal to _______

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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GATE ECE 2015 Set 3 | Question: 42
Suppose $x[n]$ is an absolutely summable discrete-time signal. Its $z$-transform is a rational function with two poles and two zeroes. The poles are at $z = \pm 2j.$ Which one of the following statements is TRUE for the signal $x[n]$? It is a finite duration signal It is a causal signal It is a non-causal signal It is a periodic signal.

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

by Milicevic3306

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GATE ECE 2015 Set 3 | Question: 44
Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1}{16}\sum_{n=0}^{15}\widetilde{x}[n] \text{exp}\big(-j\dfrac{\pi}{8} kn\big)$ for all $k .$ The value of the coefficient ܽ$a_{31}$ is _______.

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

by Milicevic3306

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GATE ECE 2015 Set 2 | Question: 5
The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the four choices given. Notation: $C$ is the set of complex numbers, ܴ$R$ is the set of purely ... $x(t)\in P$ $x(t)\in (C-R)$ the information given is not sufficient to draw any conclusion about $x(t)$

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

by Milicevic3306

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GATE ECE 2014 Set 4 | Question: 17
A Fourier transform pair is given by $\left ( \frac{2}{3} \right ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{-j6 \pi f}}{1- (\frac{2}{3} ) e^{-j2 \pi f}}$ where $u[n]$ denotes the unit step sequence. The values of $A$ is ____________

Milicevic3306 asked in Continuous-time Signals Mar 26, 2018

by Milicevic3306

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GATE ECE 2014 Set 2 | Question: 52
In the figure, $M(f)$ is the Fourier transform of the message signal $m(t)$ where $A = 100$ Hz and $B = 40$ Hz. Given $v(t)= \cos (2\pi f_{c}t)$ and $w(t)= \cos (2\pi (f_{c}+A)t)$, where $f_{c}>A$. The cutoff frequencies of both the filters are $f_{c}$. The bandwidth of the signal at the output of the modulater (in Hz) is ______.

Milicevic3306 asked in Continuous-time Signals Mar 26, 2018

by Milicevic3306

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GATE ECE 2013 | Question: 25
Let $g(t) = e^{-\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is $ e^{-\pi f^{2}}$ $ e^{-\pi f^{2}/ 2}$ $ e^{-\pi \mid f \mid }$ $ e^{-2\pi f^{2}}$

Milicevic3306 asked in Continuous-time Signals Mar 26, 2018

by Milicevic3306

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GATE ECE 2012 | Question: 31
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega$. The value of $h(0)$ is $\frac{1}{4}$ $\frac{1}{2}$ $1$ $2$

Milicevic3306 asked in Continuous-time Signals Mar 25, 2018

by Milicevic3306

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GATE ECE 2018 | Question: 14
Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is $x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}$ The same function $x(t)$ can also ... $\sum _{k=-\infty}^{\infty } \mid b_{k} \mid$ is equal to $256$ $64$ $16$ $4$

gatecse asked in Continuous-time Signals Feb 19, 2018

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GATE ECE 2017 Set 1 | Question: 31
Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is integer valued. Consider the following statements about $x(3t)$: The complex ... one of the following is correct? Only II and III are true Only I and III are true Only III is true Only I is true

admin asked in Continuous-time Signals Nov 17, 2017

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GATE ECE 2017 Set 1 | Question: 33
Let $h[n]$ ... radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.

admin asked in Continuous-time Signals Nov 17, 2017

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GATE ECE 2017 Set 1 | Question: 8
A periodic signal $x(t)$ has a trigonometric Fourier series expansion $x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )$ If $x(t)= -x(-t)=-x(t-\frac{\pi }{\omega _{0}})$, we can conclude that $a_n$ ... $n$ odd $a_n$ are zero for $n$ even and $b_n$ are zero for $n$ odd $a_n$ are zero for $n$ odd and $b_n$ are zero for $n$ even

admin asked in Continuous-time Signals Nov 17, 2017

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