Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Y(t) = x(0.5t)a)Is time shifted signalb)Is co... Start Learning for Free
Y(t) = x(0.5t)
- a)Is time shifted signal
- b)Is compressed time signal
- c)Is amplitude scaled signal
- d)Is expanded time scale signal
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Y(t) = x(0.5t)a)Is time shifted signalb)Is compressed time signalc)Is ...
When the α value is less than one in time scaling then the signal is said to be expanded or dilated
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Y(t) = x(0.5t)a)Is time shifted signalb)Is compressed time signalc)Is ...
Understanding the Signal Transformation
The given signal transformation is Y(t) = x(0.5t). To analyze this, we can categorize the effect of the transformation on the original signal x(t).
Time Scaling Concept
- Time scaling involves changing the time variable in a signal, which can either compress or expand it.
- The factor by which time is scaled determines the type of transformation:
- A factor greater than 1 expands the time axis.
- A factor less than 1 compresses the time axis.
Analyzing Y(t) = x(0.5t)
- In the expression Y(t) = x(0.5t), the time variable t is multiplied by 0.5.
- This means that for every unit of time in Y(t), the corresponding time in x(t) is halved.
Impact of Time Scaling Factor
- The time scaling factor here is 0.5, which is less than 1.
- This indicates that the signal x(t) is being expanded in time since the input (0.5t) causes the output to take longer to reach the same values as compared to x(t).
Conclusion
- Hence, Y(t) = x(0.5t) is an expanded time signal.
- It stretches the signal along the time axis, making it appear slower or more drawn out compared to the original x(t).
By understanding these principles, one can identify the correct transformation type and its implications on signal processing in Electronics and Communication Engineering.
The given signal transformation is Y(t) = x(0.5t). To analyze this, we can categorize the effect of the transformation on the original signal x(t).
Time Scaling Concept
- Time scaling involves changing the time variable in a signal, which can either compress or expand it.
- The factor by which time is scaled determines the type of transformation:
- A factor greater than 1 expands the time axis.
- A factor less than 1 compresses the time axis.
Analyzing Y(t) = x(0.5t)
- In the expression Y(t) = x(0.5t), the time variable t is multiplied by 0.5.
- This means that for every unit of time in Y(t), the corresponding time in x(t) is halved.
Impact of Time Scaling Factor
- The time scaling factor here is 0.5, which is less than 1.
- This indicates that the signal x(t) is being expanded in time since the input (0.5t) causes the output to take longer to reach the same values as compared to x(t).
Conclusion
- Hence, Y(t) = x(0.5t) is an expanded time signal.
- It stretches the signal along the time axis, making it appear slower or more drawn out compared to the original x(t).
By understanding these principles, one can identify the correct transformation type and its implications on signal processing in Electronics and Communication Engineering.
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