Question
Download Solution PDFA 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
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The sampling frequency is given by:
\(f_s = {1 \over T_s}\)
where, fs = Sampling frequency
Ts = Time period
Calculation:
Given, Y(n) = [x(n) + x(n - 1) + x(n - 2) + x(n - 4)/4]
The maximum delay in output Y(n) is due to the x(n-4).
Hence, the maximum time taken for the output to reach the final value after the input transition will be 4Ts.
\(T_s = {1 \over 100}\)
Ts = 10msec
Maximum delay = 4Ts
Maximum delay = 4× 10 ms
Maximum delay = 40 ms
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