GATE ECE

Discrete Time Signal Fourier Series Fourier Transform

Signals and Systems

(Past Years Questions)

Marks 1

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The value of $$\sum\limits_{n = 0}^\infty n {\left( {{1 \over 2}} \right)^n}$$ is ________________.
GATE ECE 2015 Set 3
A Fourier transform pair is given by $${\left( {{2 \over 3}} \right)^n}$$ u $$\left[ {n + 3} \right]\,\mathop \Leftrigh...
GATE ECE 2014 Set 4
Let x(n) = $${\left( {{1 \over 2}} \right)^n}$$ u(n), y(n) = $${x^2}$$, and Y ($$({e^{j\omega }})\,$$ be the Fourier tra...
GATE ECE 2005

Marks 2

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Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n], where X[k] = $$\sum\limits_{n = 0}^{N - 1} {x\left[ n \ri...
GATE ECE 2018
Let h[n] be the impulse response of a discrete time linear time invariant (LTI) filter. The impulse response is given by...
GATE ECE 2017 Set 1
Two discrete-time signals x [n] and h [n] are both non-zero only for n = 0, 1, 2 and are zero otherwise. It is given tha...
GATE ECE 2017 Set 1
Consider the signal $$x\left[ n \right] = 6\delta \left[ {n + 2} \right] + 3\delta \left[ {n + 1} \right] + 8\delta \lef...
GATE ECE 2016 Set 1
Let $$\widetilde x\left[ n \right]\, = \,1 + \cos \left[ {{{\pi n} \over 8}} \right]$$ be a periodic signal with period ...
GATE ECE 2015 Set 3
A 5-point sequence x [n] is given as x$$\left[ { - 3} \right]$$ =1, x$$\left[ { - 2} \right]$$ =1, x$$\left[ { - 1} \ri...
GATE ECE 2007
A sequence x(n) has non-zero values as shown in Fig. The sequence $$$y(n)=\left\{\begin{array}{l}x\left(\frac n2-1\ri...
GATE ECE 2005
A sequence x(n) has non-zero values as shown in figure. 1 The Fourier transform of y(2n) will be ...
GATE ECE 2005

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