# FSK: Selecting center frequencies and Carson's Rule

I'm implementing 2FSK and 4FSK modulation schemes for an experimental system. I'm using GNURadio, although that shouldn't affect the question.

I'm trying to figure out how the center frequency should be selected. Many 2FSK examples use a center frequency of 1700Hz, with a deviation of 500Hz, for a "space" frequency of 1200Hz and a "mark" frequency of 2200Hz.

1. How are these values arrived at, though? From my understanding, only the deviation affects the modulation index and the occupied bandwidth (Carson's rule). So, why use 1700Hz +/- 500Hz, instead of 1000Hz +/- 500Hz?

2. Is there a lower bound? i.e. would it be possible to use a center frequency of 500Hz, for a "space" at 0Hz (DC) and a "mark" at 1000Hz?

3. I'd also like to confirm how deviation is defined in 4FSK. In 2FSK, the symbol values are at fc - fd and fc + fd, where fc = center frequency and fd = frequency deviation from fc. In 4FSK, is it:

• Symbol values are at fc - 3fd, fc - fd, fc + fd, fc + 3fd, or
• Symbol values are at fc - 2fd/3, fc - fd/3, fc + fd/3, fc + 2fd/3

i.e. is fd the deviation from center to the first symbol value, or from center to the last (outermost) symbol value?

I'm trying to determine how to estimate the occupied bandwidth of a 4FSK signal using Carson's rule: BW = 2(fd + fb) where fb = bitrate, but it's unclear what the value of fd would be here in 4FSK.

1. As a concrete example: what would the occupied bandwidth be for a 4FSK signal at 50 baud (100 bits/second), where the center frequency is 2000Hz and the symbol values are at 1250Hz, 1750Hz, 2250Hz, and 2750Hz?
• Carson's Rule is predominantly used for analog FM systems and does predict occupied bandwidth for FSK. Are you doing straight FSK with square wave transitions from one frequency to the next (which has relatively poor spectral occupancy)? Often the transitions are smoothed if there is any concern with spectral occupancy (such as Gaussian-FSK). Mar 14 at 1:41
• The Wikipedia article on frequency modulation has more useful information about the bandwidth of FM than the Wikipedia article on Carson's rule. As Dan Boschen points out, Carson 's rule is predominantly used for analog FM; it does not give good approximations for FSK. Mar 14 at 1:56