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Zero-order hold used in practical reconstruction of continuous-time signals is mathematically represented as a weighted-sum of rectangular pulses shifted by:
- a)Any multiples of the sampling interval
- b)Integer multiples of the sampling interval
- c)One sampling interval
- d)1 second intervals
Correct answer is option 'B'. Can you explain this answer?
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Zero-order hold used in practical reconstruction of continuous-time si...
Explanation: Zero-order hold is used to reconstruct the continuous-time signal which is represented as a weighted sum of rectangular pulses shifted by integer multiples of the sampling interval.
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Zero-order hold used in practical reconstruction of continuous-time si...
Zero-order hold in practical reconstruction of continuous-time signals
The zero-order hold (ZOH) is a common technique used in practical reconstruction of continuous-time signals from their discrete-time samples. It is a type of interpolation method that approximates the continuous-time signal by holding each sample value for a duration equal to the sampling interval.
Mathematical representation of zero-order hold
The zero-order hold is mathematically represented as a weighted-sum of rectangular pulses shifted by integer multiples of the sampling interval.
Explanation of the correct answer (Option B)
Option B states that the rectangular pulses are shifted by integer multiples of the sampling interval. This means that each rectangular pulse used in the reconstruction process is shifted by an integral number of sampling intervals.
This choice is correct because shifting the rectangular pulses by integer multiples of the sampling interval ensures that each sample value is held for the correct duration. The ZOH technique holds each sample value for the entire duration of the sampling interval, which is achieved by shifting rectangular pulses.
Importance of shifting by integer multiples of the sampling interval
Shifting the rectangular pulses by integer multiples of the sampling interval is important because it ensures that the reconstruction accurately captures the original continuous-time signal. If the pulses were shifted by non-integer multiples or any multiples of the sampling interval, it would result in incorrect reconstruction and introduce errors in the signal.
Conclusion
In practical reconstruction of continuous-time signals using the zero-order hold technique, the rectangular pulses are mathematically represented as a weighted-sum of rectangular pulses shifted by integer multiples of the sampling interval. This choice ensures that each sample value is held for the correct duration and accurately reconstructs the original continuous-time signal.
The zero-order hold (ZOH) is a common technique used in practical reconstruction of continuous-time signals from their discrete-time samples. It is a type of interpolation method that approximates the continuous-time signal by holding each sample value for a duration equal to the sampling interval.
Mathematical representation of zero-order hold
The zero-order hold is mathematically represented as a weighted-sum of rectangular pulses shifted by integer multiples of the sampling interval.
Explanation of the correct answer (Option B)
Option B states that the rectangular pulses are shifted by integer multiples of the sampling interval. This means that each rectangular pulse used in the reconstruction process is shifted by an integral number of sampling intervals.
This choice is correct because shifting the rectangular pulses by integer multiples of the sampling interval ensures that each sample value is held for the correct duration. The ZOH technique holds each sample value for the entire duration of the sampling interval, which is achieved by shifting rectangular pulses.
Importance of shifting by integer multiples of the sampling interval
Shifting the rectangular pulses by integer multiples of the sampling interval is important because it ensures that the reconstruction accurately captures the original continuous-time signal. If the pulses were shifted by non-integer multiples or any multiples of the sampling interval, it would result in incorrect reconstruction and introduce errors in the signal.
Conclusion
In practical reconstruction of continuous-time signals using the zero-order hold technique, the rectangular pulses are mathematically represented as a weighted-sum of rectangular pulses shifted by integer multiples of the sampling interval. This choice ensures that each sample value is held for the correct duration and accurately reconstructs the original continuous-time signal.
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Zero-order hold used in practical reconstruction of continuous-time signals is mathematically represented as a weighted-sum of rectangular pulses shifted by:a)Any multiples of the sampling intervalb)Integer multiples of the sampling intervalc)One sampling intervald)1 second intervalsCorrect answer is option 'B'. Can you explain this answer?
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