# How to determine the length of a symbol in a wave?

Is there a way to determine the length of a symbol in a wave? For example, how could I determine the length of a 0 or a 1 in a 2FSK wave?

• All the answers so far have been talking about the physical length of a symbol traveling through the air. I have a feeling that you might mean "given a 2FSK signal, how can I determine the symbol rate if I don't already know it". If that's what you meant, you might want to edit your question to clarify. Apr 22, 2016 at 15:37

Well the procedure itself is not very complicated.
You'll need following things:

• Carrier frequency $F_c$ or the period
• Wavelength $\lambda$ in your environment or the speed of wave in the medium
• Symbol rate $Rs$

So let's say we have radio signal in free space (or close to it) with carrier frequency of 7075 kHz (wavelength 42.4028 m) and that we're running say RTTY at 50 Bd.

The way to think about the issue is simple: The wave moves one wavelength in one carrier cycle. So to get the length of a symbol, you need to see how many carrier cycles we have during one symbol cycle and multiply the number by the wavelength.

This gives us:

$$l = \frac{R_s}{F_c} \lambda= 6000\:\mathrm{km}$$

This is same as the wavelength of the symbol rate inside of the medium itself, but the long-way around explanation is mostly there to illustrate the thought process used given the question itself.

Say we are transmitting 50 symbols per second. You begin by transmitting a 1. Then 1/50th of a second later, you are done transmitting that 1. Now how far has the signal propagated since you started transmitting the 1? That's the "length" of the symbol.

That's simple to calculate, as the signal propagates away at the speed of light. We can just divide the speed of light by the number of symbols per second to get the length of a symbol in meters.

So with the speed of light being about 300000000 meters per second, and one second per 50 symbols:

$$\require{cancel} {3\cdot 10^8\:\text{meters}\over \cancel{\text{second}}} \cdot {1\:\cancel{\text{second}} \over 50\:\text{symbols}} = {6000000\:\text{meters} \over \text{symbol}}$$

That is, 6000 km per symbol.

You'll also see this is exactly the same calculation as for converting from frequency to wavelength, but in place of frequency (cycles per second) we use the baud rate (symbols per second).