Frequency Modulation: Periodicity & Modulation Index

[boredaxel]

For frequency modulation, will the modulated signal always be periodic? or does the periodicity depend on the modulation index? or does it depend on whether the message signal is periodic?
Thanks for any help on this

 

[MATLABdude]

This sounds a little like homework. There's a very nice illustration at the Wikipedia page:
http://en.wikipedia.org/wiki/Modulation

Consider what might be the case (AM or FM) if you had:
a) a periodic information signal, and
b) a non-periodic information signal

Remember the definition of periodic is that f(t+To)=f(t), i.e. you see the same thing repeated over, and over again.

 

[boredaxel]

From what I observed, if the information signal is periodic, the modulated signal from FM and AM will be periodic. However, if the information signal is non periodic, the modulated signal will be non periodic for AM. Please correct me if I am wrong so far.

However, I am abit unsure as to whether the FM modulated signal will be periodic for modulation index < 1 because the modulated signal from a simulation trial looks periodic to me, however, I suspect that it is not. Please enlighten me on this.

Thanks for the advice

 

[MATLABdude]

From what I observed, if the information signal is periodic, the modulated signal from FM and AM will be periodic. However, if the information signal is non periodic, the modulated signal will be non periodic for AM. Please correct me if I am wrong so far.

However, I am abit unsure as to whether the FM modulated signal will be periodic for modulation index < 1 because the modulated signal from a simulation trial looks periodic to me, however, I suspect that it is not. Please enlighten me on this.

Thanks for the advice

Your interpretation of AM is correct. For the FM, the modulation index "is a measure of the peak frequency deviation." Thus, when your modulation index < 1 (and I suspect, << 1 in your example) the frequency isn't really shifting very much, and it won't be really noticeable when you plot out a few cycles of the carrier (and probably really won't be noticeable when you plot out lots and lots of cycles and everything bands together).
http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm

 

[boredaxel]

Thanks MATLABdude, so am I right to say that for non periodic information signal, FM modulated signal is non periodic, just that it is not very noticeable?