Problem 7 on Energy and Power | Representation of Signals | Signals and Systems

TL;DR

This video explains how to calculate the energy and power of a trigonometric function using the example of a cosine term.

Transcript

hello friends in this video we are going to find out energy and or power of trigonometric function which is cosine term so x of t is a cosine which is given as 3 cos 5 omega 0 t it is just a notation given for the frequency omega 0 so it's a cosine term means it's a periodic signal so just find out energy and power so energy of any signal is given ... Read More

Key Insights

• 📡 The energy of a signal is calculated by finding the integral of the signal's square over its entire range.
• 📡 If the energy of a signal is finite, it is considered an energy signal, whereas if the energy is infinite, it is not an energy signal.
• ⌛ The power of a signal is calculated by finding the limit of (1/2t) times the integral of the signal's square over a specific time duration.
• ✊ If the power of a signal is finite, it is considered a power signal, whereas if the power is infinite, it is not a power signal.
• 🍉 The energy of a cosine term is found to be infinite, making it not an energy signal.
• ✊ However, the power of the cosine term is found to be finite, indicating that it is a power signal.
• 🇨🇨 The integral of the cosine term can be simplified using the formula cos square theta equals (1/2) times (1 + cos 2 theta).

Questions & Answers

Q: How is the energy of a signal calculated?

The energy of a signal is calculated using the formula e infinity equals the integral of x square t dt. In this case, for the given cosine term, the integral over the entire range is found to be infinite.

Q: How is the power of a signal calculated?

The power of a signal is calculated using the formula p infinity equals the limit of (1/2t) times the integral of x square t dt. For the given cosine term, the limit is taken as t approaches infinity, and the resulting finite value indicates that the signal is a power signal.

Q: Why is the energy of the cosine term infinite?

The energy of the cosine term is infinite because the integral of x square t dt over the entire range does not converge to a finite value. Hence, the energy of the signal is not finite.

Q: What does it mean for a signal to be a power signal?

A signal is considered a power signal if the power, calculated using the formula p infinity equals the limit of (1/2t) times the integral of x square t dt, yields a finite value. In the case of the cosine term, the power is found to be finite, indicating that it is a power signal.

Summary & Key Takeaways

• The video discusses the energy and power of a trigonometric function, specifically a cosine term.

• The energy of a signal is calculated using the formula e infinity equals the integral of x square t dt, and the result for the cosine term is found to be infinite.

• The power of the signal is then calculated using the formula p infinity equals the limit of (1/2t) times the integral of x square t dt, and the result is finite, indicating that the given signal is a power signal.