Transmission of Signal Through Continuous Time LTI Systems · Signals and Systems · GATE ECE

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Marks 1

GATE ECE 2022
Let x1(t) = e$$-$$t u(t) and x2(t) = u(t) $$-$$ u(t $$-$$ 2), where u( . ) denotes the unit step function. If y(t) denotes the convolution of x1(t) an...
GATE ECE 2022
The outputs of four systems (S1, S2, S3 and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure. Based on the given ...
GATE ECE 2016 Set 1
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed thr...
GATE ECE 2014 Set 4
A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose ...
GATE ECE 2013
Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) is ...
GATE ECE 2013
Let g(t) = $${e^{ - \pi {t^2}}}$$, and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the outpu...
GATE ECE 2010
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is ...
GATE ECE 2010
A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output $$y(t) = \cos \left( {2t - {\pi \over 3}} \righ...
GATE ECE 2006
In the system shown below, x(t) = (sint)u(t). In steady-state, the response y(t) will be ...
GATE ECE 2006
A low-pass filter having a frequency response $$H(j\omega )$$ = $$A(\omega ){e^{j\Phi (\omega )}}$$, does not product any phase distortion if
GATE ECE 2002
A linear phase channel with phase delay $${\tau _p}$$ and group delay $${\tau _g}$$ must have
GATE ECE 1999
The input to a channel is a band pass signal. It is obtained by linearly modulating a sinusoidal carrier with a signal- tone signal. The output of the...
GATE ECE 1996
A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a

Marks 2

GATE ECE 2016 Set 2
A continuous-time filter with transfer function $$\,H(S) = {{2s + 6} \over {{s^2} + 6s + 8}}$$ is converted to a discrete time filter with transfer fu...
GATE ECE 2016 Set 1
A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitat...
GATE ECE 2015 Set 1
In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H(f) is shown in Figu...
GATE ECE 2007
The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by
GATE ECE 2004
A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is
GATE ECE 2004
Consider the signal x(t) shown in Fig. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interv...
GATE ECE 2003
The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega $$ and C = 1.0 $$\mu F$$. Let $${t_g}$$ (f) be the group del...
GATE ECE 2003
The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega $$ and C = 1.0 $$\mu F$$. Let H(t) denote the frequency resp...
GATE ECE 2002
In Fig. m(t) = $$ = {{2\sin 2\pi t} \over t}$$, $$s(t) = \cos \,200\pi t\,\,andn(t) = {{\sin 199\pi t} \over t}$$. The output y(t) will be ...
GATE ECE 2000
A system has a phase response given by $$\phi \,(\omega )$$ where $$\omega $$ is the angular frequency. The phase delay and group delay at $$\omega $$...
GATE ECE 1999
The input to a matched filter is given by $$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{...
GATE ECE 1993
Sketch the waveform (with properly marked axes) at the output of a matched filter matched for a signal s(t), of duration T, given by $$s(t) = \left\{ ...
GATE ECE 1991
The pole-zero pattern of a certain filter is shown in the Fig. The filter must be of the following type. ...
GATE ECE 1990
The magnitude and phase transfer functions for a distortionless filter should respectively be:
GATE ECE 1988
Specify the filter type if its voltage transfer function H(s) is given by H(s) = $${{K({s^2} + {\omega _0}^2)} \over {{s^2} + ({\omega _0}/Q)s + {\o...

Marks 5

GATE ECE 2001
A base band signal g(t) band limited to 100 Hz modulates a carrier of frequency $${{f_0}}$$ Hz. The modulated signal g(t) $$\cos 2\,\pi \,{f_0}t$$ is ...
GATE ECE 1996
A signal 3 sin $$\left( {\pi \,\,{f_0}t} \right) + \,5\,\,\cos \,\,\,(3\pi \,\,{f_0}t)$$ is applied to an RC low pass filter of 3 dB cutoff frequency ...
GATE ECE 1996
An input signal A exp $$\left( { - \alpha \,t} \right)$$ u(t) with $$\alpha > 0$$ is applied to a causal filter, the impulse response of which is ...
GATE ECE 1994
A signal, f(t) = $${e^{ - at}}$$ u(t), where u(t) is the unit step function, is applied to the input of a low-pass filter having $$\left| {H(\omega )}...
GATE ECE 1993
Obtain an expression for the signal in figure, for the signal $${v_3}(t)$$ in Fig for $${v_1}(t) = 100\cos (2000\pi t) + 4\sin (200\pi t)$$. Assume ...
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