1
GATE ECE 2002
+1
-0.3
Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to
A
$$X\left( {t - 12} \right)$$
B
$$X\left( {t + 12} \right)$$
C
$$X\left( {t - 2} \right)$$
D
$$X\left( {t + 2} \right)$$
2
GATE ECE 2002
Subjective
+5
-0
A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure.
(a) Determine the autocorrelation Rxx ($$\tau$$) and the power spectral density Sxx(f).
(b) Find the output power spectral density Syy( f ).
(c) Evaluate Rxy(0) and Rxy(1/4).
3
GATE ECE 2002
+2
-0.6
If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is equal to
A
$${{ - z} \over {z - 5}}$$ and the system is stable.
B
$${z \over {z - 5}}$$ and the system is stable.
C
$${{ - z} \over {z - 5}}$$ and the system is unstable.
D
$${z \over {z - 5}}$$ and the system is unstable.
4
GATE ECE 2002
+1
-0.3
Consider a sampled signal $$y\left( t \right) = 5 \times {10^{ - 6}}\,x\left( t \right)\,\,\sum\limits_{n = - \infty }^{ + \infty } {\delta \left( {t - n{T_s}} \right)}$$

where $$x\left( t \right) = 10\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$ and
$${T_s} = 100\,\,\mu \sec .$$ When $$y\left( t \right)$$ is passed through an ideal low-pass filter with a cutoff frequency of 5 KHz, the output of the filter is

A
$$5 \times {10^{ - 6}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
B
$$5 \times {10^{ - 5}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
C
$$5 \times {10^{ - 1}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
D
$$10\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
GATE ECE Papers
2024
2023
2022
2021
2019
2018
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12