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Signals and Systems
Representation of Continuous Time Signal Fourier Series
Discrete Time Signal Fourier Series Fourier Transform
Discrete Time Signal Z Transform
Continuous Time Linear Invariant System
Transmission of Signal Through Continuous Time LTI Systems
Discrete Time Linear Time Invariant Systems
Sampling
Continuous Time Signal Laplace Transform
Discrete Fourier Transform and Fast Fourier Transform
Transmission of Signal Through Discrete Time Lti Systems
Miscellaneous
Fourier Transform
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GATE ECE
Fourier Transform
Signals and Systems
Previous Years Questions
START HERE
Marks 1
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If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation...
GATE ECE 2016 Set 3
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Which one of the following is an eight function of the class of all continuous-time, linear, time- invariant systems u(t...
GATE ECE 2016 Set 1
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The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.
GATE ECE 2016 Set 2
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Let x(t) $$ \leftrightarrow $$ X($$(j\omega )$$ BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3)...
GATE ECE 2006
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The Fourier transform of a conjugate symmetric function is always
GATE ECE 2004
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The Fourier transform F $$\left\{ {{e^{ - t}}u(t)} \right\}$$ is equal to $${1 \over {1 + j2\pi f}}$$. Therefore, $$F\le...
GATE ECE 2002
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If a signal f(t) has energy E, the energy of the signal f(2t) is equal to
GATE ECE 2001
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The Fourier Transform of the signal $$x(t) = {e^{ - 3{t^2}}}$$ is of the following form, where A and B are constants:
GATE ECE 2000
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A signal x(t) has a Fourier transform X ($$\omega $$). If x(t) is a real and odd function of t, then X($$\omega $$) is
GATE ECE 1999
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A modulated signal is given by s(t)= $${e^{ - at}}$$ cos $$\left[ {({\omega _c} + \Delta \omega )t} \right]$$ u (t), whe...
GATE ECE 1999
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The Fourier transform of a voltage of a voltage signal x(t) is X(f). The unit of |X(f)| is
GATE ECE 1998
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The Fourier transform of a function x(t) is X(f). The Fourier transform of $${{dx(t)} \over {dt}}$$ will be
GATE ECE 1998
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The amplitude spectrum of a Gaussian pulse is
GATE ECE 1998
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The function f(t) has the Fourier Transform g($$\omega $$). The Fourier Transform of $$$g(t) = \left( {\int\limits_{ - \...
GATE ECE 1997
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The Fourier transform of a real valued time signal has
GATE ECE 1996
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Marks 2
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The complex envelope of the bandpass signal $$x(t)\, = \, - \sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right)\...
GATE ECE 2015 Set 3
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The value of the integral $$\int_{ - \infty }^\infty {12\,\cos (2\pi )\,{{\sin (4\pi t)} \over {4\pi t}}\,dt\,} $$ is
GATE ECE 2015 Set 2
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For a function g(t), it is given that $$\int_{ - \infty }^\infty {g(t){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}...
GATE ECE 2014 Set 1
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The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}} $$ (5t) dt is
GATE ECE 2014 Set 2
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The Fourier transform of a signal h(t) is $$H(j\omega )$$ =(2 cos $$\omega $$) (sin 2$$\omega $$) / $$\omega $$. The val...
GATE ECE 2012
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The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr ...
GATE ECE 2008
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For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by
GATE ECE 2005
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Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2). Then Y...
GATE ECE 2004
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The Hilbert transform of $$\left[ {\cos \,{\omega _1}t + \,\sin {\omega _2}t\,} \right]$$ is
GATE ECE 2000
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If the Fourier Transfrom of a deterministic signal g(t) is G (f), then Item-1 (1) The Fourier transform of g (t - ...
GATE ECE 1997
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The power spectral density of a deterministic signal is given by $${\left[ {\sin (f)/f} \right]^2}$$, where 'f' is frequ...
GATE ECE 1997
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The autocorrelation function of an energy signal has
GATE ECE 1996
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If G(f) represents the Fourier transform of a signal g (t) which is real and odd symmetric in time, then
GATE ECE 1992
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Marks 5
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The Fourier transform $$G(\omega )$$ of the signal g(t) in Fig.(1) is given as $$G(\omega ) = {1 \over {{\omega ^2}}}({...
GATE ECE 2001
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Consider a rectangular pulse g(t) existing between $$t = \, - {T \over 2}\,and\,{T \over 2}$$. Find and sketch the pulse...
GATE ECE 1998
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A signal v(t)= [1+ m(t) ] cos $$({\omega _c}t)$$ is detected using a square law detector, having the characteristic $${v...
GATE ECE 1995
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