1
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2). GATE ECE 2004 Signals and Systems - Fourier Transform Question 11 English

Then Y(f) is

A
$$ - {1 \over 2}X(f/2){e^{ - j2\pi f}}$$
B
$$ - {1 \over 2}X(f/2){e^{j2\pi f}}$$
C
$$ - X(f/2){e^{j2\pi f}}$$
D
$$ - X(f/2){e^{ - j2\pi f}}$$
2
GATE ECE 2004
MCQ (Single Correct Answer)
+1
-0.3
The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {n - 7} \right],$$ where $$u\left[ n \right]$$ is the unit step sequence. The above system is
A
stable but not causal.
B
stable and causal.
C
causal but unstable.
D
unstable and not causal.
3
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
A causal LTI system is described by the difference equation $$2y\left[ n \right] = ay\left[ {n - 2} \right] - 2x\left[ n \right] + \beta x\left[ {n - 1} \right].$$ The system is stable only if
A
$$\left| \alpha \right| = 2,\,\left| \beta \right| < 2$$
B
$$\left| \alpha \right| > 2,\,\left| \beta \right| > 2$$
C
$$\left| \alpha \right| < 2$$, any value of $$\beta $$
D
$$\left| \beta \right| < 2,$$ any value of $$\alpha $$
4
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
The impulse response $$h\left[ n \right]$$ of a linear time invariant system is given as
$$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} & {n = 1, - 1} \cr {4\sqrt 2 ,} & {n = 2, - 2} \cr {0,} & {otherwise} \cr } } \right.$$

If the input to the above system is the sequence $${e^{j\pi n/4}},$$ then the output is

A
$$4\sqrt 2 \,{\mkern 1mu} {e^{j\,\pi \,n\,\,/\,4}}$$
B
$$4\sqrt 2 \,{\mkern 1mu} {e^{ - j\,\pi \,n\,/4}}$$
C
$$4{\mkern 1mu} {e^{j\,\pi \,n\,/4}}$$
D
$$ - 4{\mkern 1mu} {e^{j\,\pi \,n\,/4}}$$
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12