Time Shifting, Scaling, and Reversal of Signals Quiz Quiz

Challenge your understanding of signal transformations by answering questions about time shifting, scaling, and reversal. This quiz covers key concepts, mathematical operations, and signal behavior scenarios, using well-explained examples relevant to digital and analog signal processing.

1. Identifying Time Shifting

   If x(t) is shifted to the right by 3 units in time, which of the following expressions correctly represents this operation?

   1. x(-t + 3)
   2. x(t - 3)
   3. x(3t)
   4. x(t + 3)

   Explanation: Shifting a signal to the right by 3 units is represented as x(t - 3), because time shifting by a positive value subtracts from the argument. x(t + 3) shifts the signal left, which is the opposite operation. x(3t) represents time scaling, not shifting. x(-t + 3) combines reversal and shifting, but not a pure right shift.

2. Understanding Time Reversal

   Given a signal x(t), which new signal describes its time-reversed version?

   1. x(-t)
   2. x(t+1)
   3. x(-t-1)
   4. x(2t)

   Explanation: Time reversal means flipping the signal about the vertical axis, which is achieved using x(-t). x(t+1) shifts the signal left, not reverses it. x(-t-1) combines reversal and shifting but is not a pure reversal. x(2t) compresses the signal in time, not reverses it.

3. Time Scaling Application

   If the signal x(t) is compressed to half of its duration, what is the correct mathematical expression for this scaled signal?

   1. x(t/2)
   2. 2x(t)
   3. x(2t)
   4. x(t)+2

   Explanation: Compressing a signal to half its original duration involves scaling its time variable by a factor greater than one, in this case, x(2t). x(t/2) would stretch the signal, making it last twice as long. 2x(t) increases the amplitude, not the duration. x(t)+2 simply adds a constant to the output and does not affect time scaling.

4. Combined Time Shifting and Reversal

   For the signal x(t), how is the transformation represented where the signal is first time-reversed and then shifted to the right by 4 units?

   1. x(t - 4)
   2. x(-t + 4)
   3. x(-t - 4)
   4. x(t + 4)

   Explanation: Time reversal is first applied, giving x(-t), and shifting right by 4 units modifies it to x(-t + 4). x(-t - 4) shifts left after reversal, which is incorrect. x(t - 4) is only right shifting. x(t + 4) is only left shifting, with no reversal involved.

5. Effect of Time Scaling

   If the original signal is x(t), which of the following describes the effect of x(0.5t) on the signal’s behavior?

   1. It stretches the signal in time by a factor of two
   2. It compresses the signal by a factor of two
   3. It delays the signal by 0.5 units
   4. It reverses the signal

   Explanation: Applying x(0.5t) causes the signal to play out over twice the original duration, effectively stretching it. Delaying the signal by 0.5 units would require a time-shifting term, not scaling. Compression by a factor of two would use x(2t). Time reversal is represented by x(-t), not with a scaling factor.