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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Questions  >  Y(t) = x2(t) is _[ ]A) Linear time invariant ... Start Learning for Free
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Y(t) = x
2(t) is _[ ]A) Linear time invariant system B) Non-Linear time invariant system
C) Linear time variant system D) Non-Causal System?
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Y(t) = x2(t) is _[ ]A) Linear time invariant system B) Non-Linear time...
Y(t) = x^2(t) is a Non-Linear time invariant system


Explanation:

1. Definition of a Linear System

A system is considered linear if it satisfies the following two properties:


  • Superposition: The response to a sum of inputs is equal to the sum of the responses to each individual input.

  • Homogeneity: Scaling the input signal scales the output signal proportionally.



2. Definition of a Time-Invariant System

A system is considered time-invariant if its behavior does not change over time. In other words, if the input signal is delayed or advanced in time, the output signal should be delayed or advanced by the same amount.


3. Analysis of Y(t) = x^2(t)

Let's analyze the given system:

Y(t) = x^2(t)


3.1 Linearity Test

We can test the linearity of the system by applying the superposition property:


  • Superposition: The response to a sum of inputs is equal to the sum of the responses to each individual input.


If we consider two input signals x1(t) and x2(t), the output for the sum of these signals would be:

Y(t) = x1^2(t) + x2^2(t)

Since the output is not equal to the sum of the responses to each individual input, the given system is non-linear.


3.2 Time-Invariance Test

We can test the time-invariance of the system by analyzing the effect of a time delay on the input and output signals.

If we consider a time-delayed input signal x(t - τ), the output for this delayed input would be:

Y(t - τ) = [x(t - τ)]^2

The output signal is not equal to Y(t) delayed by τ, indicating that the given system is time-variant.


4. Conclusion

Based on the above analysis, we can conclude that the system described by Y(t) = x^2(t) is a non-linear time-variant system.
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Y(t) = x2(t) is _[ ]A) Linear time invariant system B) Non-Linear time invariant systemC) Linear time variant system D) Non-Causal System?
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