GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

The function x(t) is shown in Fig. Even and odd parts of a unit-step function u(t) are respectively. GATE ECE 2005 Signals and Systems - Miscellaneous Question 19 English

GATE ECE 2005 Signals and Systems - Miscellaneous Question 19 English

$${1 \over 2},\,{1 \over 2}x(t)$$

$$-{1 \over 2},\,{1 \over 2}x(t)$$

$${1 \over 2},\,-{1 \over 2}x(t)$$

$$-{1 \over 2},\,-{1 \over 2}x(t)$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

A signal x(n)$$ = \sin ({\omega _0}\,n + \phi )$$ is the input to a linear time-invariant system having a frequency response $$H({e^{j\omega }})$$.If the output of the system is $$Ax(n - {n_0})$$, then the most general form of $$\angle H({e^{j\omega }})$$ will be

$$ - {n_0}{\omega _0} + \beta $$ for any arbitrary real $$\beta $$

$$ - {n_0}{\omega _0} + 2\pi k$$ for any arbitrary integer k

$${n_0}{\omega _0} + 2\pi k$$ for any arbitrary integer k

$$-{n_0}{\omega _0} + \phi $$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by

$${1 \over 2}\,x\left( {{t \over 2}} \right){e^{j3\pi t}}$$

$${1 \over 3}\,x\left( {{t \over 3}} \right){e^{ - j4\pi t/3}}$$

$$3\,x(3t){e^{ - j4\pi t}}$$

$$x(3t + 2)$$