Questions & Answers of Linear Time-Invariant (LTI) Systems

Weightage of Linear Time-Invariant (LTI) Systems

Total 18 Questions have been asked from Linear Time-Invariant (LTI) Systems topic of Signals and Systems subject in previous GATE papers. Average marks 1.50.

Which one of the following is an eigen function of the class of all continuous-time, linear, timeinvariant systems (ut denotes the unit-step function)?

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form

$\sum\limits_{k=1}^3a_k\;\cos\left(k\omega_0t\right),\;\mathrm{where}\;a_k\neq0\;,\omega_0\neq0.$

The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

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 corresponding time responses for $t\geq0;$
X: Impulse       P:1-e-t/T
Y: Unit step    Q:t-T1-e-t/T
Z: Ramp   R:e-t/T

 

If the signal xt=sintπt*sintπt with *  denoting the convolution operation, then x(t) is equal to

The result of the convolution $ \mathrm x(-\mathrm t)\;\ast\;\mathrm\delta(-\mathrm t-{\mathrm t}_0) $ is

The impulse response of an LTI system can be obtained by

A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x\left[n\right]$, the response $y\left[n\right]$ is

 

The complex envelope of the bandpass signal xt=-2sinπt/5πt/5sin(πt-π4),centered about f=12Hz, is

A continuous, linear time-invariant filter has an impulse response h(t) described by

ht=3for 0t30otherwise

When a constant input of value 5 is applied to this filter, the steady state output is_____.

For a function g(t), it is given that -+gte-jwtdt=ωe-2ω2 for any real value ω.
If yt=-tgtdτ, , then -tytdt  is

Consider a discrete-time signal

xn=nfor 0n100otherwise.

If y[n] is the convolution of x[n] with itself, the value of y[4] is _________.

The input -3e2tut, where ut is the unit step function, is applied to a system with transfer function s-2s+3. If the initial value of the output is −2, then the value of the output at steady state is _______.

The sequence xn=0.5nun, where un is the unit step sequence, is convolved with itself to obtain yn. Then n=-+yn is _______.

The DFT of a vector abcd is the vector αβγδ . Consider the product

pqrs=abcdabcddabccdabbcda

The DFT of the vector pqrs is a scaled version of

Let y[n] denote the convolution of h[n] and g[n], where h[n]=(1/2)n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

A system is defined by its impulse response h(n) = 2n u(n − 2). The system is

The impulse response ht of a linear time-invariant continuous time system is described by ht=expαtut+expβtu-t, where ut denotes the unit step function, and α and β are real constants. This system is stable if

A discrete time linear shift-invariant system has an impulse response h[n] with h[0]=1, h[1]=-1. h[2]=-2, and zero otherwise. The system is given an input sequence x[n] with x[0]=x[2]=1, and zero otherwise. The number of nonzero samples in the outp ut sequence y[n], and the value of y[2] are, respectively