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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?
Most Upvoted Answer
A digital measuring instrument employs a sampling rate of 100 samples/...
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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Community Answer
A digital measuring instrument employs a sampling rate of 100 samples/...
Calculation of Maximum Time for Output to Reach Final Value
1. Given Parameters:
- Sampling rate = 100 samples/second
- Difference equation for averaging: Y(n) = [x(n) + x(n-1) + x(n-2) + x(n-4)] / 4
2. Analysis:
- To determine the time taken for the output to reach the final value after a step input, we need to consider the time taken for the input transition to propagate through the averaging process.
3. Time Delay Calculation:
- The time delay introduced by the difference equation can be calculated by considering the number of samples required for the step input to propagate through the averaging process.
- In this case, since the input is averaged over 4 samples (n, n-1, n-2, n-4), the time delay introduced by the difference equation is 4 samples / 100 samples/second = 0.04 seconds = 40 ms.
4. Maximum Time for Output to Reach Final Value:
- The time taken for the output to reach the final value after the input transition is the sum of the time delay introduced by the averaging process and the settling time of the system.
- Since the time delay introduced by the difference equation is 40 ms, and the settling time of the system is negligible, the maximum time for the output to reach the final value after the input transition is 40 ms.
Therefore, the correct answer is option 'B' - 40 ms.
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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 isa)20 msb)40 msc)80 msd)∞Correct answer is option 'B'. Can you explain this answer?
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