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The signal x(t) = t u(t) is a
- a)Power signal with P∞ = 1
- b)Energy signal with E∞ = 0
- c)Power signal with P∞ = 0
- d)Neither an energy signal nor a power signal
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The signal x(t) = t u(t) is aa)Power signal with P= 1b)Energy signal w...
The signal x(t) = t u(t) is Neither an energy signal nor a power signal.
If the signal energy in one period is infinite, then both the power and the total energy are infinite. Consequently, the signal is neither an energy signal nor a power signal. ( )ti . the signal energy in and the power loss is the same as the power of the periodic signal .
Most Upvoted Answer
The signal x(t) = t u(t) is aa)Power signal with P= 1b)Energy signal w...
Explanation:
The given signal is x(t) = t u(t), where u(t) is the unit step function.
To determine whether the signal is an energy signal or a power signal, we need to calculate its energy and power.
Energy of the signal:
The energy of a signal is defined as:
E = ∫ |x(t)|^2 dt
where |.| denotes the magnitude.
For the given signal, we have:
E = ∫ |t u(t)|^2 dt
= ∫ t^2 u(t)^2 dt
= ∫ t^2 dt (since u(t)^2 = u(t) for all t)
= [t^3/3]0∞
= ∞
Since the energy of the signal is infinite, it is not an energy signal.
Power of the signal:
The power of a signal is defined as:
P = lim T→∞ (1/2T) ∫-T^T |x(t)|^2 dt
For the given signal, we have:
P = lim T→∞ (1/2T) ∫-T^T |t u(t)|^2 dt
= lim T→∞ (1/2T) ∫0^T t^2 dt (since u(-t) = 0 for t > 0)
= lim T→∞ (1/2T) [T^3/3]
= lim T→∞ T^2/6
= ∞
Since the power of the signal is also infinite, it is not a power signal.
Therefore, the given signal is neither an energy signal nor a power signal.
The given signal is x(t) = t u(t), where u(t) is the unit step function.
To determine whether the signal is an energy signal or a power signal, we need to calculate its energy and power.
Energy of the signal:
The energy of a signal is defined as:
E = ∫ |x(t)|^2 dt
where |.| denotes the magnitude.
For the given signal, we have:
E = ∫ |t u(t)|^2 dt
= ∫ t^2 u(t)^2 dt
= ∫ t^2 dt (since u(t)^2 = u(t) for all t)
= [t^3/3]0∞
= ∞
Since the energy of the signal is infinite, it is not an energy signal.
Power of the signal:
The power of a signal is defined as:
P = lim T→∞ (1/2T) ∫-T^T |x(t)|^2 dt
For the given signal, we have:
P = lim T→∞ (1/2T) ∫-T^T |t u(t)|^2 dt
= lim T→∞ (1/2T) ∫0^T t^2 dt (since u(-t) = 0 for t > 0)
= lim T→∞ (1/2T) [T^3/3]
= lim T→∞ T^2/6
= ∞
Since the power of the signal is also infinite, it is not a power signal.
Therefore, the given signal is neither an energy signal nor a power signal.
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The signal x(t) = t u(t) is aa)Power signal with P= 1b)Energy signal w...
Determine the power and energy signal of the following. find whether the signals are energy or power signal
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