Impulse Response

The relation between the input current (I) and the output voltage (V) of a circuit is governed by the equation: $C \frac{dV}{dt} = I(t) - m(t)$. The circuit is excited by $I(t) = q...

Consider the discrete-time system below with input x[n] and output y[n]. In the figure, h₁[n] and h₂[n] denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also,...

A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5t) is applied to another causal and stable LTI system with...

For a causal discrete-time LTI system with transfer function $H(z) = \frac{2z^2+3}{(z+\frac{1}{3})(z-\frac{1}{3})}$ which of the following statements is/are true?

Let an input x[n] having discrete time Fourier transform $X(e^{j\Omega}) = 1 - e^{-j\Omega} + 2e^{-3j\Omega}$ be passed through an LTI system. The frequency response of the LTI sys...

Let x(t) = 10 cos(10.5Wt) be passed through an LTI system having impulse response h(t) = π (sin Wt / πt)^2 cos 10Wt. The output of the system is

The output $y[n]$ of a discrete - time system for an input $x[n]$ is $$ y[n]=\max\limits_{-\infty \leq k \leq n}|x[k]| $$ The unit impulse response of the system is

Let h[n] be the impulse response of a discrete time linear time invariant (LTI) filter. The impulse response is given by h(0)= $${1 \over 3};h\left[ 1 \right] = {1 \over 3};h\left[...

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 excitation signals X, Y, Z with the c...

The impulse response of an LTI system can be obtained by

The impulse response of an LTI system can be obtained by

A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \le 3} \cr {0\,otherwise} \cr } } \...

The input-output relationship of a causal stable LTI system is given as 𝑦[𝑛] = 𝛼 𝑦[𝑛 − 1] + $$\beta $$ x[n]. If the impulse response h[n] of this system satisfies the conditio...

Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the following three statements. S1: The system is stable. S2: $${{h\l...

Two system with impulse responses h 1 (t) and h 2 (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of the step response at t = 2 is

The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is

Consider the differential equation $${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$ with $$y\left( t...

If the unit step response of a network is $$(1-e^{-\alpha t})$$, then its unit impulse response is

A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is

An input x(t) = exp( -2t) u(t) + $$\delta $$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The output is

Two discrete time systems with impulse responses $${h_1}\left[ n \right]\, = \delta \left[ {n - 1} \right]$$ and $${h_2}\left[ n \right]\, = \delta \left[ {n - 2} \right]$$ are con...

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applie...

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4, and one simple zero at s = - 1. A unit step u(t)...

A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$ $$ = 1,\,\,h\left[ 1 \right]\,\, = - 1,\,\,h\left[ 2 \right...

The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\left( t \right)\,\,\, + \,\,\e...

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function. The frequency response H(ω) of the sy...

The unit impulse response of a system is: $$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit step input is equal to

Let $$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}^ * p\left( t \right)$$ where $$ * $$ denotes convolution and...

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$. With the value of "a" set for phase-margin of $$\pi $$/4, the...

Let g(t) = p(t) * p(t), where * denotes convolution and p(t) = u(t) - (t-1) with u(t) being the unit step function. The impulse response of filter matched to the singal s(t) = g(t)...

A solution for the differential equation $$\mathop x\limits^. $$(t) + 2 x (t) = $$\delta (t)$$ with intial condition $$x({0^ - }) = 0$$ is

Which of the following can be impulse response of a causal system?

The z transform of a system is H(z) = $${z \over {z - 0.2}}$$ . If the ROC is $$\left| {z\,} \right|$$ < 0.2, then the impulse response of the system is

The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {...

The impulse response $$h\left[ n \right]$$ of a linear time invariant system is given as $$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} & {n = 1, - 1} \cr {4\sqrt 2 ,} & {...

A sequence $$x\left( n \right)$$ with the $$z$$-transform $$X\left( z \right)$$ $$ = {z^4} + {z^2} - 2z + 2 - 3{z^{ - 4}}$$ is applied as an input to a linear, time-invariant syste...

The impulse response function of four linear system S1, S2, S3, S4 are given respectively by $${h_1}$$(t), = 1; $${h_2}$$(t), = U(t); $${h_3}(t)\, = \,{{U(t)} \over {t + 1}}$$; $${...

The transfer function of a system is given by $$H\left( s \right) = {1 \over {{s^2}\left( {s - 2} \right)}}$$. The impulse response of the system is

A linear time invariant system has an impulse response e 2t , t > 0. If the initial conditions are zero and the input is e 3t , the output for t > 0 is

A certain linear, time-invariant system has the state and output representation shown below: $$$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}...

A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero and the input is $${e^{3t}}$$, the output for $$t\, > \,0$$ is

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e -at u(t), a > 0 will be

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e -at u(t), a>0 will be

Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right. In the case of a linear time invariant system List - 1 (1) Poles in the right hal...

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 A exp $$\,( - \alpha \,\,t)$$. Det...

A system having a unit impulse response $$h\left( n \right)$$ = $$u\left( n \right)$$ is excited by a signal $$x\left( n \right)$$ $$ = \,{\alpha ^n}\,\,u\left( n \right).\,$$ Dete...

Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is

The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ The response of this network to...

A rectangular pulse existing between t = 0 and t = T and having an amplitude A is to be received by a matched filter (a) Draw the impulse response of the matched filter labeling al...