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# How to find out if this signal is FM ?

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#### SherlockBenedict

##### Member level 4
I want to know if this signal is AM or FM or any other kind of that?

Here's the signal

cosωct + 0.5 cos ωmt sinωct

Note that: ωc is the carrier frequency and ωm 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.

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

### SherlockBenedict

Points: 2
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

How did you get 5 radians?

Thanks a lot

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

So the phase should be

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

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