Periodicity Properties of Continuous Time Signal  Representation of Signals  Signals and Systems  Summary and Q&A
TL;DR
Learn about the concept of periodicity for continuous and discrete time signals and how to determine their fundamental time periods.
Key Insights
 ⌛ Continuous time signals can be periodic or nonperiodic, depending on their fundamental time periods.
 ⌛ Sampled versions of continuous time signals can also be periodic, with the same fundamental time periods as the continuous time signals, as long as n is a ratio of two integers.
 ⌛ Discrete time signals can have different fundamental time periods than their continuous time counterparts, but only if n is a ratio of two integers.
Transcript
in this video we are going to learn concept of periodicity for continuous time and related discrete time signals let's consider three examples so i will consider the example number one where where x of t is given as cos 2 pi by 12 into t as we know we can compare this standard equation to get the value of omega so comparing cos omega t will give me... Read More
Questions & Answers
Q: What does it mean for a signal to be periodic?
A periodic signal repeats itself after a certain interval, known as the fundamental time period.
Q: How do you determine the fundamental time period of a continuous time signal?
By comparing the equation of the signal with the standard equation for a cosine signal, you can find the value of omega, which is equal to 2 pi divided by the time period.
Q: Can a discrete time signal be periodic even if its continuous time counterpart is not?
Yes, a discrete time signal can be periodic even if its continuous time counterpart is not. The fundamental time period of the discrete time signal is determined by the numerator of the ratio of the discrete time period.
Q: What is the condition for a discrete time signal to be periodic?
The condition for a discrete time signal to be periodic is that the sampling variable, n, must be a ratio of two integers.
Summary & Key Takeaways

The video discusses three examples of periodic signals, where the first example has a fundamental time period of 12, the second example has a fundamental time period of 31/4, and the third example is not periodic.

The sampled versions of the continuous time signals are also discussed, with the first two examples being periodic in the discrete domain with the same fundamental time periods as in the continuous domain.

The third example, however, is not periodic in the discrete domain.