How to find out if this signal is FM ?

[SherlockBenedict]

I want to know if this signal is AM or FM or any other kind of that?

Here's the signal

cosω_ct + 0.5 cos ω_mt sinω_ct


Note that: ω_c is the carrier frequency and ω_m is the message/modulating frequency
Please see this carefully and tell me if the signal is AM or FM. The book says that it is FM but I don't get that.

Thanks in advance

 

[zorro]

Think in a phasorial picture.
In-phase component (I) is the function that multiplies cos(ωct) i.e. 1 .
Quadrature component (Q) is the function that multiplies sin(ωct) i.e. 0.5*cos(ωmt).
The resultant phasor has almost constant amplitude and a phase that is practically 0.5*cos(ωmt) radians .
It is a PM signal whose modulating signal is cos(ωmt) and peak phase deviation 0-5 rad .
Alternatively, it can be a FM signal whose modulating signal is sin(ωmt) .
Regards

Z

 

[SherlockBenedict]

Think in a phasorial picture.
In-phase component (I) is the function that multiplies cos(ωct) i.e. 1 .
Quadrature component (Q) is the function that multiplies sin(ωct) i.e. 0.5*cos(ωmt).
The resultant phasor has almost constant amplitude and a phase that is practically 0.5*cos(ωmt) radians .
It is a PM signal whose modulating signal is cos(ωmt) and peak phase deviation 0-5 rad .
Alternatively, it can be a FM signal whose modulating signal is sin(ωmt) .
Regards

Z

I can understand now but I don't get the peak phase deviation. I understand that the minimum phase shift is 0 rad. But the maximum seems to for me-

Maximum value of quadrature is 0.5
Value of inphase is 1

So the phase should be

tan-1(0.5/1)= 0.46 radians

How did you get 5 radians?

Thanks a lot

 

[sandipm14]

Dear please check below link i think your answer is in this linck.

so please check this.

https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part12/page1.html

 

[zorro]

...
Maximum value of quadrature is 0.5
Value of inphase is 1

So the phase should be

tan-1(0.5/1)= 0.46 radians

How did you get 5 radians?

You're right. I meant 0.5 rad, not 0-5 rad . (In was a typo; in my keyboard the '.' is next to the '-' .)
I used the approximation tan^-1(x)≈x valid for "small" x.
Regards

Z