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2-Level GFSK - Receiver IF Filer Bandwidth Calculation

Hello all,

Can somebody please explain how to calculate a receiver IF Filer bandwidth ?

I've looked through the internet and found two ways...I can't tell which one is the right one.

For example:

Transmitter parameters are:

Data rate: 500bps

Peak deviation: 250Hz

Modulation index = 1

Modulation method is 2-Level GFSK

One way of calculating the above is:

Carson's rule:   BW=2(peak deviation + max modulation frequency)

The maximum modulation frequency is 250Hz = 500bps (assuming that a 500bps square wave fed into a bt=0.5 gaussian filter results a 250Hz sine wave)

BW is = 2(250 + 250) = 1KHz 

The other way is using bessel chart:

If the modulation index equal 1, so there is 3 sidebands (according to the chart)

BW= 2* (max modulation frequency) * (number of sidebands)

BW= 2 * 250 * 3 = 1.5KHz (which is 0.5KHz wider then carson's rule calculation)

Which is correct?

Thank you,

Nir