Increase the order of data hold willa)improve the stability of the systemb)decrease the time delayc)increase the time delayd)increase the time constantCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Data Hold

Data hold is a process of generating a continuous-time signal h(t) from a discrete-time sequence x(kT).

The signal h(t) during the time interval kT ≤ t ≤ (k + 1)T may be approximated by a polynomial in τ as follows:

h(kT + τ ) = a_nτⁿ + a_n−1τⁿ⁻¹ + ··· + a₁τ + a₀

Where 0 ≤ τ ≤ T

Note: h(kT) = x(kT)

h(kT + τ ) = a_nτⁿ + a_n−1τⁿ⁻¹ + ··· + a₁τ + x(kT)

If the data hold circuit is an n^th-order polynomial extrapolator, it is called an n^th-order hold. It uses the past n + 1 discrete data x((k − n)T), x((k − n + 1)T), ··· , x(kT) to generate h(kT + τ ).

Conclusion:

As the order of the data hold increases the circuit order(n) also increases which leads to the further increase in the time delay because it has to use past n + 1 samples.

Option C is correct.

Answer

Explanation:

Increasing the order of data hold will result in an increase in time delay. This can be explained as follows:

1. Data Hold:
Data hold refers to the ability of a system to hold the data or maintain its state for a certain period of time. It is an important characteristic of a system, especially in control systems and signal processing.

2. System Stability:
System stability refers to the ability of a system to maintain a steady-state or equilibrium condition in the presence of disturbances. A stable system is desirable as it ensures that the output remains within acceptable bounds.

3. Time Delay:
Time delay is the amount of time it takes for a system to respond to a change in the input. It is an important parameter in control systems as it affects the performance and stability of the system.

4. Time Constant:
Time constant refers to the time it takes for a system to reach approximately 63.2% of its final value in response to a step input. It is a measure of the system's response speed.

Effect of Increasing the Order of Data Hold:
When the order of data hold is increased, it means that the system takes longer to hold the data or maintain its state. This results in an increase in the time delay of the system.

1. Stability:
Increasing the time delay can have a destabilizing effect on the system. This is because a high time delay can introduce phase shifts and oscillations in the system's response. These phase shifts and oscillations can lead to instability, where the output of the system grows without bound.

2. Time Delay:
Increasing the time delay can also increase the overall time it takes for the system to respond to changes in the input. This means that the system will take longer to reach its steady-state or equilibrium condition.

3. Time Constant:
Increasing the time delay can also increase the time constant of the system. This means that the system will take longer to reach approximately 63.2% of its final value in response to a step input.

Therefore, increasing the order of data hold will result in an increase in the time delay, which can have a destabilizing effect on the system and increase the overall response time of the system. Hence, option 'C' is the correct answer.

Answer

Data Hold

Data hold is a process of generating a continuous-time signal h(t) from a discrete-time sequence x(kT).

The signal h(t) during the time interval kT ≤ t ≤ (k + 1)T may be approximated by a polynomial in τ as follows:

h(kT + τ ) = a_nτⁿ + a_n−1τⁿ⁻¹ + ··· + a₁τ + a₀

Where 0 ≤ τ ≤ T

Note: h(kT) = x(kT)

h(kT + τ ) = a_nτⁿ + a_n−1τⁿ⁻¹ + ··· + a₁τ + x(kT)

If the data hold circuit is an n^th-order polynomial extrapolator, it is called an n^th-order hold. It uses the past n + 1 discrete data x((k − n)T), x((k − n + 1)T), ··· , x(kT) to generate h(kT + τ ).

Conclusion:

As the order of the data hold increases the circuit order(n) also increases which leads to the further increase in the time delay because it has to use past n + 1 samples.

Option C is correct.

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