Signals and Systems
LTI Systems
LTI System Properties
Questions mapped to LTI System Properties under LTI Systems.
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IncorrectSelected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is
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Sign in to UnlockThe continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system . The output is observed to be the continuous-time unit step signal . Which one of the following statements is true?
Every bounded input signal applied to results in a bounded output signal.
It is possible to find a bounded input signal which when applied to results in an unbounded output signal.
On applying any input signal to , the output signal is always bounded.
On applying any input signal to the output signal is always unbounded.
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Sign in to UnlockWhich of the following statement(s) is/are true?
If an LTI system is causal, it is stable.
A discrete time LTI system is causal if and only if its response to a step input is 0 for .
If a discrete time system has an impulse response of finite duration the system is stable.
If the impulse response for all , then the LTI system is stable.
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Sign in to UnlockLet a causal LTI system be governed by the following differential equation , where x(t) and y(t) are the input and output respectively. Its impulse response is
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Sign in to UnlockConsider the system as shown below
where . The system is
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Sign in to UnlockIf the input x(t) and output y(t) of a system are related as y(t) = max (0, x(t)), then the system is
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Sign in to UnlockConsider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:
The poles of this system are at
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Sign in to UnlockWhich of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:
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Sign in to UnlockThe Symbols, a and T, represent positive quantities, and is the unit step function. Which one of the following impulse responses is not the output of a causal linear time-invariant system?
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Sign in to UnlockA continuous-time input signal x(t) is an Eigen function of an LTI system, if the output is
, where k is an Eigen value
, where k is an Eigen function and is a complex exponential signal
due, where is a complex exponential signal
, where k is an Eigen function and is a frequency response of the system
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Sign in to UnlockConsider the system with following input-output relation
Where x [n] is the input and y [n] is the output. The system is
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Sign in to UnlockLet a causal LTI system be characterized by the following differential equation, with initial rest condition
Where, x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)
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Sign in to UnlockConsider a continuous-time system with input x(t) and output y(t) given by
This system is
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Sign in to UnlockFor linear time invariant systems, that are Bounded input Bounded output stable, which one of the following statements is TRUE?
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Sign in to UnlockThe z – transform of a sequence is given as. If y[n] is the first difference of x[n], then Y(z) is given by
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Sign in to UnlockAn input signal is sampled with a sampling frequency of 400Hz and applied to the system whose transfer function is represented by
Where, N represents the number of samples per cycle. The output y(n) of the system under steady state is
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Sign in to UnlockThe input x(t) and output y(t) of a system are related as. The system is
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Sign in to UnlockThe system represented by the input-output relationship
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Sign in to UnlockA cascade of 3 Linear Time Invariant systems is causal and unstable. From this, we conclude that
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Sign in to UnlockA signal is the input to a real Linear Time Invariant system. Given K and φ are constants, the output of the system will be of the form where
need not be equal to but equal to
ν need not be equal to but equal to
equal to and equal to
need not be equal and need not be equal to
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Sign in to UnlockThe Impulse response of a causal linear time variant system is given as h(t). Now consider the following two statements:
Statement (I): Principle of superposition holds
Statement (II): h(t) = 0 for t < 0.
Which one of the following statements is correct'?
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Sign in to UnlockA system with input x(t) and output y(t) is defined by the input-output relation:
The system will be
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Sign in to UnlockA continuous time system is described by , where y(t) is the output and x(t) is the input. y(t) is bounded
Only when x(t) is bounded
Only when x(t) is non-negative
Only for if x(t) is bounded for
Even when x(t) is not bounded.
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Sign in to Unlocks(t) is step response and h(t) is impulse response of a system. Its response y(t) for any input u(t) is given by
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