Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t...
reduces to 1 – 2t, which is a strictly decreasing function.
Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t...
Monotonic Signal Explanation:
Monotonic signals are signals that either always increase or always decrease, without any reversals or fluctuations. Let's analyze each given signal to determine which one is monotonic.
Signal Analysis:
- x(t) = t3 – 2t: This signal is not monotonic because it contains both increasing and decreasing segments. It has a cubic term that can cause the signal to change direction.
- x(t) = sin(t): This signal is periodic and oscillates between -1 and 1 as t varies. It is not monotonic because it does not strictly increase or decrease.
- x(t) = sin^2(2t) + cos^2(2t) – 2t: This signal simplifies to 1 - 2t, which is a linear function decreasing with time. It is a monotonic signal as it always decreases without any reversals.
- x(t) = log(cos(t)): This signal is not monotonic as the logarithmic function can introduce fluctuations and changes in direction.
Conclusion:
Therefore, the signal x(t) = sin^2(2t) + cos^2(2t) – 2t is the only monotonic signal among the given options.