1
GATE ECE 2015 Set 3
Numerical
+2
-0
Let $$\widetilde x\left[ n \right]\, = \,1 + \cos \left[ {{{\pi n} \over 8}} \right]$$ be a periodic signal with period 16. Its DFS coefficients are defined by
$${a_k}$$ = $${1 \over {16}}\sum\limits_{n = 0}^{15} {\widetilde x} \left[ n \right]\exp \left( { - j{\pi \over 8}kn} \right)$$ for all k. The value of the coeffcients $${a_{31}}$$ is _____________________.
$${a_k}$$ = $${1 \over {16}}\sum\limits_{n = 0}^{15} {\widetilde x} \left[ n \right]\exp \left( { - j{\pi \over 8}kn} \right)$$ for all k. The value of the coeffcients $${a_{31}}$$ is _____________________.
Your input ____
2
GATE ECE 2007
MCQ (Single Correct Answer)
+2
-0.6
A 5-point sequence x [n] is given as x$$\left[ { - 3} \right]$$ =1, x$$\left[ { - 2} \right]$$ =1, x$$\left[ { - 1} \right]$$ =0, x$$\left[ { - 0} \right]$$ = 5, x$$\left[ { - 1} \right]$$ = 1. Let X$$({e^{j\omega }})\,$$ denote the discrete - time Fourier transform of x(n). The value of $$\int\limits_{ - \pi }^\pi x $$
($$({e^{j\omega }})\,$$ d$$\omega $$ is
3
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
A sequence x(n) has non-zero values as shown in Fig.
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

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
4
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
A sequence x(n) has non-zero values as shown in figure. 1
The Fourier transform of y(2n) will be

The Fourier transform of y(2n) will be
Questions Asked from Discrete Time Signal Fourier Series Fourier Transform (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Representation of Continuous Time Signal Fourier Series
Fourier Transform
Continuous Time Signal Laplace Transform
Discrete Time Signal Fourier Series Fourier Transform
Discrete Fourier Transform and Fast Fourier Transform
Discrete Time Signal Z Transform
Continuous Time Linear Invariant System
Discrete Time Linear Time Invariant Systems
Transmission of Signal Through Continuous Time LTI Systems
Sampling
Transmission of Signal Through Discrete Time Lti Systems
Miscellaneous
Communications
Electromagnetics
General Aptitude