Are two signals that make up a periodic signal necessarily periodic?

In summary, a periodic signal is a type of signal that repeats itself over time with a constant period. It cannot be made up of non-periodic signals, as it is composed of identical copies of a single basic signal. Two signals can make up a periodic signal by having the same fundamental period or a simple mathematical relationship between their periods. The amplitudes and phases of the signals do not affect the periodicity of the resulting signal. Real-life examples include musical notes and digital signals in computer communication.
  • #1
ChickenChakuro
32
0

Homework Statement



If a(t) is periodic and is composition of two signals such that a(t) = b(t) + c(t), then are b(t) and c(t) necessarily periodic?

2. The attempt at a solution

I think that b(t) and c(t) must be! Is this correct?
 
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  • #2
No. b(t)=sin(t)+t. c(t)=sin(t)-t. Wasn't that easy?
 
  • #3
Dick said:
No. b(t)=sin(t)+t. c(t)=sin(t)-t. Wasn't that easy?

Indeed it was. Thanks for your help!
 

1. What is a periodic signal?

A periodic signal is a type of signal that repeats itself over time, with a constant period or interval between each repetition.

2. Can a periodic signal be made up of non-periodic signals?

No, a periodic signal is composed of identical copies of a single basic signal, also known as a fundamental period. If the basic signal is not periodic, then the resulting periodic signal will not be either.

3. How can two signals make up a periodic signal?

Two signals can make up a periodic signal by having the same fundamental period, or by having a simple mathematical relationship between their periods. For example, if one signal has a period of 2 seconds and the other has a period of 4 seconds, the resulting periodic signal will have a period of 4 seconds.

4. What if the two signals have different amplitudes or phases?

The amplitudes and phases of the two signals do not affect the periodicity of the resulting signal. As long as the fundamental periods or periods relationship is the same, the resulting signal will still be periodic.

5. Are there any real-life examples of periodic signals composed of two signals?

Yes, there are many real-life examples of periodic signals that are composed of two or more signals. For instance, musical notes are periodic signals made up of multiple sine waves at different frequencies, and digital signals in computer communication are periodic signals made up of a combination of high and low voltage levels.

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