Signals and Systems
LTI Systems
Practice questions from LTI Systems.
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IncorrectConsider the discrete-time system below with input and output . In the figure, and denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, is the unit impulse, and .
Assuming , the overall system (denoted by the dashed box) is _________.
We see that:
o/p has a constant term in addition, system fails Superposition (additivity), & hence is non linear
{Reason: is linear and is non-linear}
- Delay by
Thus, system is time variant
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(0.5 t) is applied to another causal and stable LTI system with impulse response h(0.5t). The resulting output is_________.
Consider a system with input and output . The system is
For causality,
We have,
At
i.e. present value of output depends on future value of input, hence it is non-causal.
For Time Variant:
Delay the input,
…(i)
Delay the output,
…(ii)
i.e. equations (i) (ii)
Hence, it is time variant system.
So the system is Non causal & time varying option (b) is correct.