Bandwidth, symbol rate and data rate

What it is

A signal needs bandwidth: a slice of spectrum its sidebands occupy. How fast you can send information through a slice depends on how wide it is and how far the signal stands above the noise. Understanding those two limits explains why CW is narrow but slow, why a video link needs megahertz, and why FT8 works when you cannot hear a thing.

Symbols and bits

A symbol is one state of the carrier, held briefly. Symbol rate (baud) is how often it changes. The rate at which the waveform changes decides how much spectrum it fills, so bandwidth tracks the symbol rate. Bit rate is symbol rate times bits per symbol, so carrying more bits per symbol (see Digital modulation: FSK, PSK and QAM) raises the data rate without widening the signal. Shaping the transitions smoothly keeps the bandwidth close to the symbol rate; abrupt transitions spread it wider.

Even simple Morse follows this: its width grows with keying speed, and with how sharply the keying is shaped. A sharp edge makes clicks. A rough rule is about 4 Hz per word per minute: 13 wpm is about 52 Hz wide.

The Shannon limit

Claude Shannon showed that no matter how clever the scheme, the maximum error-free rate through a noisy channel is C = B × log₂(1 + S/N), with S/N as a plain ratio, not dB. Two consequences:

• At a fixed S/N, doubling bandwidth doubles the capacity. But a wider channel also admits twice the noise, so unless power rises, S/N falls by 3 dB.
• Raising SNR helps only logarithmically: at good SNR, each doubling of signal power (3 dB) adds about one bit per second per hertz.

At low SNR capacity is small but never zero, which is what weak-signal modes exploit. FT8 occupies about 50 Hz and decodes down to roughly −20 dB signal to noise in the usual 2.5 kHz reference. That is about −3 dB within its own 50 Hz, where the Shannon limit is near 30 bit/s. FT8 carries about 6 bit/s of message, comfortably inside the limit. Real modes sit below the limit; none can exceed it.

Mode	Bandwidth	Why
FT8, PSK31	31 to 50 Hz	very slow symbols
CW	tens to a few hundred Hz	depends on speed and shaping
SSB voice	2.4 to 3 kHz	the voice itself
FM voice	10 to 16 kHz	deviation plus audio
Digital TV	MHz	many bits per second

In practice

• A narrower mode (or receiver filter) hears weaker signals, because half the bandwidth admits half the noise power: 3 dB better. See Noise and signal-to-noise ratio.
• Slow is a feature: weak-signal modes buy sensitivity with time, and with error correction.
• Space signals by about their own width, so neighbours don't overlap. See Band plans.

Related

• Digital modulation: FSK, PSK and QAMHow bits become tones and phase shifts.
• Error detection and correctionParity, CRC and forward error correction.
• Noise and signal-to-noise ratioWhere noise comes from and why SNR decides what you can copy.
• Time domain, frequency domain and FourierSeeing a signal as its sine-wave ingredients.
• Digital modes overviewThe landscape of data modes and what each is for.
• FT8 and FT4Weak-signal 15-second and 7.5-second modes.