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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
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GATE ECE
Miscellaneous
Signals and Systems
Previous Years Questions
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Marks 1
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The waveform of a periodic signal x(t) is shown in the figure. A signal g(t) is defined by $$g(t) = x\left( {{{t - 1...
GATE ECE 2015 Set 1
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Consider the function $$g(t) = {e^{ - t}}\,\,\,\sin (2\pi t)\,u(t)$$ where u(t) is the unit step function. The area unde...
GATE ECE 2015 Set 3
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A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is
GATE ECE 2014 Set 1
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The phase response of a passband waveform at receiver is given by $$\varphi \,(f) = - 2\,\pi \,\alpha \,(f - {f_c}) - \...
GATE ECE 2014 Set 3
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For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin $${\rm{(500t + }}\,\pi /4)$$, the fundamental frequency in...
GATE ECE 2013
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Consider an angle modutated signal $$x(t) = 6\,\,\cos \,[2\,\pi \, \times {10^6}t + 2\sin (8000\pi t)\,4\cos (8000\pi t...
GATE ECE 2010
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The Dirac delta function $$\delta (t)$$ is defined as
GATE ECE 2006
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A solution for the differential equation $$\mathop x\limits^. $$(t) + 2 x (t) = $$\delta (t)$$ with intial condition $$x...
GATE ECE 2006
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The function x(t) is shown in Fig. Even and odd parts of a unit-step function u(t) are respectively. ...
GATE ECE 2005
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Let $$\delta (t)$$ denote the delta function. The value of the the integral $$\int\limits_{ - \infty }^\infty {\delta (...
GATE ECE 2001
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The ACF of a rectangular pulse of duration T is
GATE ECE 1998
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Marks 2
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The complex envelope of the bandpass signal $$x(t) = - \sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,\...
GATE ECE 2015 Set 3
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An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in stead...
GATE ECE 2009
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In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be: ...
GATE ECE 2007
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A Hilbert transformer is a
GATE ECE 2007
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As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$
GATE ECE 2006
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Match the following and choose the correct combination. GROUP 1 E- continuous and aperiodic signal F- continuous ...
GATE ECE 2005
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The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}...
GATE ECE 2005
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The derivative of the symmetric function drawn in Fig .1 will look like ...
GATE ECE 2005
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Consider the sequence $$x[n] = [ - \,4 - \,j5,\,\mathop {1 + j2}\limits_ \uparrow ,\,\,4]$$ The conjugate anti-symm...
GATE ECE 2004
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Match each of the items, A, B and C, with an appropriate item from 1, 2, 3, 4 and 5 A. Fourier transform of a Gaussian...
GATE ECE 1995
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