1
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-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
The Fourier transform of y(2n) will be
A
$${e^{ - j2\omega }}\left[ {\cos {\mkern 1mu} 4\omega + {\mkern 1mu} 2\cos \,2\omega + 2} \right]$$
B
$$\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$
C
$${e^{ - j\omega }}\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$
D
$${e^{j2\omega }}\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$
2
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-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 10 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
A
GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 10 English Option 1
B
GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 10 English Option 2
C
GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 10 English Option 3
D
GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 10 English Option 4
3
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-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
A
$${1 \over 4}$$
B
2
C
4
D
$${4 \over 3 }$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists?
A
Re(s) > a+2
B
Re(s) > a+7
C
Re(s) < 2
D
Re(s) > a+5
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