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Consider the system as shown below: where y(t) = x(et). The system is...
GATE EE 2022
Let a causal LTI system be governed by the following differential equation $$y(t) + {1 \over 4}{{dy} \over {dt}} = 2x(t)... GATE EE 2022 Consider a continuous-time system with input x(t) and output y(t) given by$$y\left(t\right)=x\left(t\right)\cos\left(t\...
GATE EE 2016 Set 1
The impulse response g(t) of a system G, is as shown in Figure (a). What is the maximum value attained by the impulse re...
GATE EE 2015 Set 1
Consider an LTI system with transfer function $$H\left(s\right)=\frac1{s\left(s+4\right)}$$.If the input to the system i...
GATE EE 2014 Set 2
x(t) is nonzero only for $$T_x\;&lt;\;t\;&lt;\;T_x^1$$ , and similarly, y(t) is nonzero only for $$T_y\;&lt;\;t\;&lt;\;T... GATE EE 2014 Set 1 Consider an LTI system with impulse response$$h\left(t\right)=e^{-5t}u\left(t\right)$$. If the output of the system is... GATE EE 2014 Set 2 The impulse response of a system is h(t) = tu(t). For an input u(t − 1), the output is GATE EE 2013 Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the ca... GATE EE 2013 Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is ... GATE EE 2013 A low–pass filter with a cut-off frequency of 30 Hz is cascaded with a high-pass filter with a cut-off frequency of 20 H... GATE EE 2011 Given two continuous time signals$$x\left(t\right)=e^{-t}$$and$$y\left(t\right)=e^{-2t}$$which exist for t &gt; 0, t... GATE EE 2011 The system represented by the input-output relationship$$y\left(t\right)=\int_{-\infty}^{5t}x\left(\tau\right)d\tau$$, ... GATE EE 2010 For the system$$\frac2{\left(s+1\right)}$$, the approximate time taken for a step response to reach 98% of its final va... GATE EE 2010 A linear Time Invariant system with an impulse response$$h(t)$$produces output$$y(t)$$when input$$x(t)$$is applied... GATE EE 2009 The impulse response of a causal linear time-invariant system is given as$$h(t)$$. Now consider the following two state... GATE EE 2008 A signal$${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$is the input to a real Linear Time Invariant system. Give... GATE EE 2008 A signal$${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$is the input to a real Linear Time Invariant system. Give... GATE EE 2008 Let a signal$${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$be applied to a stable linear time-invariant sys... GATE EE 2007$$s(t)$$is step response and$$h(t)$$is impulse response of a system. Its response$$y(t)$$for any input$$u(t)$$is ... GATE EE 2002 If$$f(t)$$is the step-response of a linear time-invariant system, then its impulse response is given by ___________ GATE EE 1994$$s(t)$$is step response and$$h(t)$$is impulse response of a system. Its response$$y(t)$$for any input$$u(t)$$is ... GATE EE 1993 ## Marks 2 More For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE? GATE EE 2015 Set 2 The impulse response of a continuous time system is given by h(t) =$$\delta$$(t − 1) +$$\delta$$(t − 3). The value of ... GATE EE 2013 L et y[n] denote the convolution of h[n] and g[n], where$$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$and g[n] ... GATE EE 2012 The input x(t) and output y(t) of a system are related as$$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\ta...
GATE EE 2012
The response h(t) of a linear time invariant system to an impulse $$\delta\left(t\right)$$, under initially relaxed cond...
GATE EE 2011
Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the ...
GATE EE 2010
The $$z$$$$-$$ transform of a signal $$x\left[ n \right]$$ is given by $$4{z^{ - 3}} + 3{z^{ - 1}} + 2 - 6{z^2} + 2{z^3}... GATE EE 2009 A cascade of 3 Linear Time Invariant systems is casual and unstable. From this, we conclude that GATE EE 2009 A system with input$$x(t)$$and output$$y(t)$$is defined by the input$$-$$output relation:$$y\left( t \right) = \...
GATE EE 2008
The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}.$$ ...
GATE EE 2008
A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha$$ is a real constant $$\left( {\sin \,c... GATE EE 2008 A signal is processed by a causal filter with transfer function$$G(s).$$For a distortion free output signal waveform, ... GATE EE 2007 Consider the discrete-time system shown in the figure where the impulse response of$$G\left( z \right)$$is$$g\left( ...
GATE EE 2007
A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, ...
GATE EE 2007
$$X\left( z \right) = 1 - 3\,\,{z^{ - 1}},\,\,Y\left( z \right) = 1 + 2\,\,{z^{ - 2}}$$ are $$Z$$-transforms of two sign...
GATE EE 2007
A continuous-time system is described by $$y\left( t \right) = {e^{ - |x\left( t \right)|}},$$ where $$y(t)$$ is the out...
GATE EE 2006
$$x\left[ n \right] = 0;\,n &lt; - 1,\,n &gt; 0,\,x\left[ { - 1} \right] = - 1,\,x\left[ 0 \right]$$ $$\,\,\,\,\,\,\,\... GATE EE 2006$$y\left[ n \right]$$denotes the output and$$x\left[ n \right]$$denotes the input of a discrete-time system given by ... GATE EE 2006 A discrete real all pass system has a pole at$$z = 2\angle {30^ \circ };\,$$it, therefore, GATE EE 2006 In the system shown in Fig. the input$$x\left( t \right) = \sin t.$$In the steady-state, the response$$y(t)$$will be... GATE EE 2004 Given the relationship between the input$$u(t)$$and the output$$y(t)$$to be$$y\left( t \right) = \int\limits_0^t {\...
GATE EE 2001

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Match the following transfer functions and impulse responses Transfer functions \eqalign{ &amp; \left( a \right)\,\,... GATE EE 1992 ## Marks 5 More A single input single output system withy$$as output and$$u$$as input, is described by$$\${{{d^2}y} \over {d{t^2}...
GATE EE 2002
A first order system is initially at rest and excited by a step input at time $$t=0.$$ Its output becomes $$1.1$$ $$V$$ ...
GATE EE 1997
The impulse response of a network is $$h\left( t \right) = 1$$ for $$0 \le t &lt; 1$$ and zero otherwise. Sketch the im...
GATE EE 1992

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