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In recursive systems, which of the following is caused because of the nonlinearities due to the finite-precision arithmetic operations?
- a)Periodic oscillations in the input
- b)Non-Periodic oscillations in the input
- c)Non-Periodic oscillations in the output
- d)Periodic oscillations in the output
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In recursive systems, which of the following is caused because of the ...
Explanation: In the recursive systems, the nonlinearities due to the finite-precision arithmetic operations often cause periodic oscillations to occur in the output even when the input sequence is zero or some non zero constant value.
Most Upvoted Answer
In recursive systems, which of the following is caused because of the ...
Explanation:
Recursive systems are systems in which the output depends not only on the current input but also on the previous output. These systems can be represented by difference equations, and the solutions to these equations are sequences of numbers that depend on the initial conditions.
Nonlinearities due to the finite-precision arithmetic operations can cause problems in recursive systems. These nonlinearities arise because computers can only represent numbers with a finite number of bits, which leads to round-off errors and truncation errors.
One of the problems that can arise in recursive systems because of these nonlinearities is periodic oscillations in the output. This happens when the system becomes unstable and starts oscillating between two or more values. The oscillations are periodic because they repeat after a certain number of iterations.
Causes of periodic oscillations in the output:
1. Nonlinearities due to finite-precision arithmetic operations: As mentioned earlier, computers can only represent numbers with a finite number of bits. This can lead to round-off errors and truncation errors, which can cause the system to become unstable.
2. Nonlinearities in the system itself: Nonlinearities in the system, such as saturation, can also cause the system to become unstable and start oscillating.
3. Initial conditions: The initial conditions of the system can also play a role in causing periodic oscillations in the output. If the initial conditions are such that the system is close to an unstable equilibrium point, then the system can become unstable and start oscillating.
Conclusion:
In conclusion, periodic oscillations in the output of recursive systems can be caused by nonlinearities due to finite-precision arithmetic operations, nonlinearities in the system itself, and initial conditions. It is important to be aware of these issues when designing and analyzing recursive systems.
Recursive systems are systems in which the output depends not only on the current input but also on the previous output. These systems can be represented by difference equations, and the solutions to these equations are sequences of numbers that depend on the initial conditions.
Nonlinearities due to the finite-precision arithmetic operations can cause problems in recursive systems. These nonlinearities arise because computers can only represent numbers with a finite number of bits, which leads to round-off errors and truncation errors.
One of the problems that can arise in recursive systems because of these nonlinearities is periodic oscillations in the output. This happens when the system becomes unstable and starts oscillating between two or more values. The oscillations are periodic because they repeat after a certain number of iterations.
Causes of periodic oscillations in the output:
1. Nonlinearities due to finite-precision arithmetic operations: As mentioned earlier, computers can only represent numbers with a finite number of bits. This can lead to round-off errors and truncation errors, which can cause the system to become unstable.
2. Nonlinearities in the system itself: Nonlinearities in the system, such as saturation, can also cause the system to become unstable and start oscillating.
3. Initial conditions: The initial conditions of the system can also play a role in causing periodic oscillations in the output. If the initial conditions are such that the system is close to an unstable equilibrium point, then the system can become unstable and start oscillating.
Conclusion:
In conclusion, periodic oscillations in the output of recursive systems can be caused by nonlinearities due to finite-precision arithmetic operations, nonlinearities in the system itself, and initial conditions. It is important to be aware of these issues when designing and analyzing recursive systems.
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In recursive systems, which of the following is caused because of the nonlinearities due to the finite-precision arithmetic operations?a)Periodic oscillations in the inputb)Non-Periodic oscillations in the inputc)Non-Periodic oscillations in the outputd)Periodic oscillations in the outputCorrect answer is option 'D'. Can you explain this answer?
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