# Confused in Bit rate, Symbol rate, Sample rate and Data rate

I'm using GMSK modulation to send $300 \ \rm bits$ and assuming $1 \ \rm bit/symbol$. $BT$ product is $0.5$. Sampling frequency is $100\ \rm kHz$ and bandwidth of the signal is $28 \ \rm kHz$.

• (a) Is bit rate calculated as $BT/B = 0.5/28\rm k$ ?
• (b) Here, symbol rate = bit rate ?
• (c) The sample rate of input will be equal sampling frequency i.e. $100\ \rm kHz$?
• (d) How can I calculate data rate ?

The $BT$ product is linked to the single-side $-3\rm dB$ down bandwidth and the bit rate $R_b$ with the relation below: $$BT = \frac{f_{-\rm 3 dB}}{R_b}$$ Assuming you have a single-side $-3\rm dB$ bandwidth, you can extract your bit rate as: $$R_b = \frac{f_{-\rm 3 dB}}{BT}$$ Also see the answer to this question. For more on GMSK see this paper $^1$ and this paper $^2$.

You have one bit per symbol, meaning for every bit you have one symbol. And their rate should be in that proportion as well. Or see it this way, \begin{align} \text{For} \ \ &n \ \ \text{bits you have} \ \ n \ \ \text{symbols}\\ \implies \text{for} \ \ &\Delta n \ \ \text{bits you have} \ \ \Delta n \ \ \text{symbols}\\ \implies \text{for} \ \ &\frac{\Delta n \ \rm bits }{\Delta t} \ \ \text{you have} \ \ \frac{\Delta n \ \rm symbols}{\Delta t} \end{align}

See the sampling rate as the rate at which you are having your samples, and this value is in $\rm Hz$, or basically $$\frac{\Delta n \ \rm Samples}{\Delta t}$$ The $\Delta t$s above are normally given as $1 \ \rm second$. The sampling rate is the number of samples per second, also known as sampling frequency (in $\rm Hz$).

Generally speaking, your bit rate is your data rate. The answer to this question details more on this.

You can use the maths and plug in your numbers.

$[1]$: A. Linz and A. Hendrickson, "Efficient implementation of an I-Q GMSK modulator," in IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 43, no. 1, pp. 14-23, Jan 1996.

$[2]$: K. Murota and K. Hirade, "GMSK Modulation for Digital Mobile Radio Telephony," in IEEE Transactions on Communications, vol. 29, no. 7, pp. 1044-1050, Jul 1981.

• I didn't get the sample rate part. Is sample rate = sampling frequency? As as far as I know, sampling frequency is defined as number of samples per second. And in your answer above, you've said that sample rate is the rate at which you're having your samples. Isn't it one and the same thing? Mar 9 '18 at 6:40
• The rate at which you're having your samples, i.e. how many samples over time, in this case how many samples per seconds. Let me update my answer. Mar 9 '18 at 6:47