GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

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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

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

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

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

$$x(3t + 2)$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

Which of the following can be impulse response of a causal system?

GATE ECE 2005 Signals and Systems - Continuous Time Linear Invariant System Question 43 English Option 1

GATE ECE 2005 Signals and Systems - Continuous Time Linear Invariant System Question 43 English Option 2

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}} \right)^n}u( - n - 1)$$ must be

$$\left| {z\,} \right| < {5 \over 6}$$

$$\left| {z\,} \right| > {6 \over 5}$$

$${5 \over 6} < \left| {z\,} \right| < {6 \over 5}$$

$${6 \over 5} < \left| {z\,} \right| < \infty $$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

A sequence x(n) has non-zero values as shown in figure. 1 GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 9 English

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 9 English

The Fourier transform of y(2n) will be

$${e^{ - j2\omega }}\left[ {\cos {\mkern 1mu} 4\omega + {\mkern 1mu} 2\cos \,2\omega + 2} \right]$$

$$\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$

$${e^{ - j\omega }}\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$

$${e^{j2\omega }}\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$

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