Simulation of FM with multiple harmonics

[ACiDUser]

Hello!

I need to simulate FM signal, that will carry such informations as music.

I read many articles about FM basics, but everywhere was described the

simplest FM modulation using only one single SINe harmonic with equation:

FM = A*Cos(2*pi*Fc*t + M*Sin(2*pi*Fm*t))

where: A - amplitude, Fc - carrier frequency, M - modulation index, Fm - message

frequency.

A = 1, Fc = 60, M = 5, Fm = 5.

I tried adding one more harmonic like this: FM = A*Cos(2*pi*Fc*t +

M*(Sin(2*pi*Fm*t)+Sin(2*pi*3*Fm*t)) with 3 times greater frequency - but it seems

to be incorrect way, because I can recover message with single Sine message, but

with two - I get corrupted signal.

When we listen music - we hear many frequencies in same time (60Hz bass tones,

middle frequencies and high frequency sounds up to 15KHz) I want to know how this

FM modulation differs when using many harmonics for a message signal. What I might

done incorrect?

Thanks in advance.

 

[nl5]

Does it work right with just third harmonic:
FM = A*Cos(2*pi*Fc*t + M*Sin(2*pi*3*Fm*t))
?

 

[ACiDUser]

No... there is a strange phase shift

see below

 

[FvM]

To start with a simple point, your signal definition is specifying phase rather than frequency modulation. This may be important, cause the respective modulation index calculates different. Furthermore, if your generated signals look strange or are undetectable, you most likely exceeded the maximum modulation index for linear modulation. But I didn't check in detail. However, using a meaningful modulation index, the signal would be detectable.

 

[ACiDUser]

Thanks for response.

I read that in todays radios use modulation index of 5. And this normally influence at bandwidth of signal. And what is strange about picture - Highest FM Signal Frequency should be directly at the highest Message signal value. And as I see signals are shifted by phase. I can't just understand what might cause this shift.

 

[nl5]

To start with a simple point, your signal definition is specifying phase rather than frequency modulation.

ACiDUser, are you sure you are not mixing phase and frequency modulation. Since phase is integral of frequency, you can easily get what you see on the graph.

 

[ACiDUser]

To start with a simple point, your signal definition is specifying phase rather than frequency modulation.

ACiDUser, are you sure you are not mixing phase and frequency modulation. Since phase is integral of frequency, you can easily get what you see on the graph.

Maybe you're right. I must at first integrate my message signal with respect to time.