# 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?