Frequency-Shift Keying (FSK)

What is Frequency-Shift Keying?

Frequency-Shift Keying (FSK) is a digital modulation technique in which the transmitter selects a carrier frequency from a defined set to represent each symbol. In binary FSK, one frequency represents binary '1' and another represents binary '0'. The selected frequency is the information-bearing parameter.

In FSK, the amplitude of the can remain constant, which reduces sensitivity to amplitude noise and permits nonlinear power amplification. The phase need not remain continuous at symbol boundaries: ordinary switched FSK can have phase discontinuities, whereas Continuous Phase FSK (CPFSK) preserves phase continuity. This distinction affects the spectrum relative to Amplitude-Shift Keying (ASK).

The Basics of Binary FSK (BFSK)

Binary FSK uses two distinct frequencies. The names mark and space come from teleprinter signaling and identify the symbols assigned to each tone:

Mark Frequency ( $f_1$ ):Represents binary '1'. In the convention used here, it is the higher frequency.
Space Frequency ( $f_2$ ):Represents binary '0'. In the same convention, it is the lower frequency.

With this assignment, a high modulating level selects the mark tone for binary '1', so the signal frequency satisfies $f_1 > f_n$ . A low level selects the space tone for binary '0', so the signal frequency satisfies $f_2 < f_n$ .

Key Parameters and Formulas

The FSK signal can be described with the following parameters:

Carrier Frequency ( $f_n$ )

This is the center frequency around which the two tones are placed. It is the arithmetic mean of the mark and space frequencies.

$f_n = \frac{f_1 + f_2}{2}$

Frequency Deviation ( $\Delta f$ )

With $f_1 > f_2$ , this is the maximum shift from the center frequency. It equals half the difference between the mark and space frequencies.

$\Delta f = \frac{f_1 - f_2}{2}$

The tone separation, meaning the difference between the mark and space frequencies, is $|f_1-f_2| = 2\Delta f$ . Some references use $\Delta f$ for the full separation, so the convention should be stated with the formula.

Average Signal Power ( $P_{tot}$ )

For a sinusoidal carrier with peak voltage amplitude ( $U_n$ ) across a normalized 1-ohm load, constant amplitude gives constant average power:

$P_{tot} = \frac{1}{2} U_n^2$

For a load of resistance $R$ , use $P_{tot} = \frac{U_n^2}{2R}$ . The first formula is the special case $R=1$ .

FSK as a Form of Frequency Modulation (FM)

FSK is a digital form of . Analog FM varies the instantaneous frequency according to a continuous signal, such as audio. FSK selects discrete frequencies according to digital symbols, often represented by rectangular pulses.

Switching independent oscillators can introduce phase discontinuities and large spectral sidelobes. A Continuous Phase FSK (CPFSK) modulator integrates the frequency deviation so that phase remains continuous across symbol changes. MSK and GMSK are specific CPFSK or CPM schemes with additional pulse shaping.

Advantages, Disadvantages, and Applications

Advantages

Amplitude-noise tolerance: A constant envelope avoids amplitude changes from representing symbols and can be used with nonlinear power amplifiers.
Simplicity: FSK modulators and demodulators can use separate oscillators, filters, or frequency discriminators, depending on the receiver design.
Constant power: The constant envelope keeps the average RF power stable when the amplifier preserves that envelope.

Disadvantages

Bandwidth use: Basic FSK usually needs more occupied bandwidth than PSK or QAM for the same bit rate and error target.

Common Applications

FSK appears in systems whose spectrum allocation and receiver design suit its constant envelope:

Early telephone-line modems (e.g., Bell 103 standard at 300 bps).
Caller ID systems, which use FSK in many deployments; DTMF appears in some signaling variants.
Low-power radio systems and license-free bands.
Amateur radio, especially for data modes like RTTY (Radio Teletype).
Some RFID systems.