Does the use of pre-emphasis filter in FM transmitter increase the transmission signal bandwidth?

Question

I am self learning the use of pre-emphasis from The Open University courses, and it states the following:

The bandwidth of FM with and without pre-emphasis filter is the same, which is given by \$2(m+1)W\$, where \$m\$ is the modulation index in FM and \$W\$ is the bandwidth of the message signal in the unit of Hz.

[Quoted from Unit 4, ELEC S211,Fundamentals of Communication Technology, The Open University of Hong Kong]

The following explanation is also given:

Since the bandwidths of FM with and without pre-emphasis are both calculated by Carson's rule, the use of filter does not affect the transmission bandwidth of the signal.

[Quoted from Unit 4, ELEC S211,Fundamentals of Communication Technology, The Open University of Hong Kong]

However, I think it increases the transmission bandwidth since:

$$ m=\frac{\Delta}{W}=\frac{f_{d}A_{peak}}{W} $$

where \$f_{d}\$ is the frequency sensitivity in the unit of Hz per unit amplitude and \$A_{peak}\$ the peak amplitude of the message signal.

As you amplify the high frequency component of the message signal, the \$A_{peak}\$ increases and hence \$m\$ increases. This will certainly increase the transmission bandwidth as there are more sidebands now due to the increased \$m\$.

Is there something wrong in my reasoning?

Answer 1

Not necessarily.

Even if you amplify high frequencies of the message, you can change the total amplitude of the pre-emphasized message to be lower, or anything you want.

You can normalize/limit the amplitudes so the original message and pre-emphasized messages have the same maximum amplitude, for some reference signal.

If the message is speech, it does not even contain much high frequencies. So it might not change the peak amplitude by much.

One thing to note is that the pre-emphasis is already built in to the spec - you are not even modulating the orignal message, but the pre-emphasized message, so your system that outputs pre-emphasized signal and the system that takes it in for FM modulation are already matched to be compatible with each other, no matter what the actual amplitude is, there is a level of amplitude that matches the peak voltage where peak FM frequency deviation happens.