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A digital measuring instrument employs a sampling rate of 100 samples/second. The sampled input x(n) is averaged using the difference equation:
Y (n) =[x (n)+x (n-1)+x(n-2)+x(n-4)/4] For a step input, the maximum time taken for the output to reach the final value after the input transition is 
  • a)
    20 ms
  • b)
    40 ms
  • c)
    80 ms
  • d)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A digital measuring instrument employs a sampling rate of 100 samples/...
Explanation: Since output y depends on input, such as no delay, delay by 1 unit, and delay by 2 unit, delay by 4 unit, so it will sum all the samples after 4 Ts (maximum delay), to get one sample of y[n].
T =40 msec.
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Most Upvoted Answer
A digital measuring instrument employs a sampling rate of 100 samples/...


Analysis:

To determine the time taken for the output to reach the final value after a step input, we need to analyze the difference equation provided and understand the behavior of the system.

Sampling Rate:

Given sampling rate = 100 samples/second, which means the input is sampled every 1/100 seconds or 10 ms.

Difference Equation:

The given difference equation for averaging the sampled input is:
Y(n) = [x(n) + x(n-1) + x(n-2) + x(n-4)] / 4

Step Input Response:

For a step input, the output response will depend on the number of samples considered in the averaging process. In this case, the averaging involves the current sample and the three previous samples (n, n-1, n-2, n-4).

Time Constant:

The time constant of the system can be approximated as the time taken for the output to reach approximately 63.2% of the final value. In this case, the time constant can be estimated to be around 4 sampling periods.

Maximum Time Taken:

Since each sampling period is 10 ms, the maximum time taken for the output to reach the final value after the input transition can be estimated as 4 * 10 ms = 40 ms.

Therefore, the correct answer is option B) 40 ms.
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