GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

Let x(n) = $${\left( {{1 \over 2}} \right)^n}$$ u(n), y(n) = $${x^2}$$, and Y ($$({e^{j\omega }})\,$$ be the Fourier transform of y(n). Then Y ($$({e^{jo}})$$ is

$${1 \over 4}$$

$${4 \over 3 }$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

In what range should Re(s) remain so that the Laplace transform of the function e^(a+2)t+5 exists?

Re(s) > a+2

Re(s) > a+7

Re(s) < 2

Re(s) > a+5

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

A sequence x(n) has non-zero values as shown in Fig. GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 8 English

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 8 English

The sequence $$$y(n)=\left\{\begin{array}{l}x\left(\frac n2-1\right)\;\;\;for\;n\;even\\0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;for\;n\;odd\end{array}\right.$$$
will be

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 8 English Option 1

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 8 English Option 2

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

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

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

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

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

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