GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

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 7 English

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 7 English

The Fourier transform of y(2n) will be

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

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

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

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

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)

-0.3

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)

-0.6

The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: y(t) = 0.5 x $$(t - {t_d} + T) + \,x\,(t - {t_d}) + 0.5\,x(t - {t_d} - T)$$. The filter transfer function $$H(\omega )$$ of such a system is given by

$$(1 + \cos \omega T){e^{ - j\omega {t_d}}}$$

$$(1 + 0.5\cos \omega T){e^{ - j\omega {t_d}}}$$

$$(1 + \cos \omega T){e^{j\omega {t_d}}}$$

$$(1 - 0.5\cos \omega T){e^{ - j\omega {t_d}}}$$

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