Periodicity Properties of Continuous Time Signal | Representation of Signals | Signals and Systems | Summary and Q&A

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April 4, 2022
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Periodicity Properties of Continuous Time Signal | Representation of Signals | Signals and Systems

TL;DR

Learn about the concept of periodicity for continuous and discrete time signals and how to determine their fundamental time periods.

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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.

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