Frequency-Shift Keying (FSK)

Digital modulation by switching between discrete frequency levels.

What is Frequency-Shift Keying?

Frequency-Shift Keying (FSK) is a digital modulation technique where data is represented by changes in the frequency of a carrier wave. Think of it like quickly switching between two different radio stations to send a message: one station's frequency represents a binary '1', and the other station's frequency represents a binary '0'.

In FSK, the amplitude and phase of the remain constant, making the technique highly resilient to amplitude-based noise and interference, which is a significant advantage over Amplitude-Shift Keying (ASK).

The Basics of Binary FSK (BFSK)

The simplest and most common form of FSK is Binary FSK, which uses two distinct frequencies. These are often referred to by their historical teleprinter names:

Mark Frequency ( $f_1$ ): Represents the binary '1'. This is typically the higher frequency.
Space Frequency ( $f_2$ ): Represents the binary '0'. This is typically the lower frequency.

As seen in the diagram, when the modulating signal is high (representing a '1'), the modulated signal oscillates at the higher mark frequency ( $f_1 > f_n$ ). When the modulating signal is low (representing a '0'), the modulated signal oscillates at the lower space frequency ( $f_2 < f_n$ ).

Interactive FSK – Modulated Signal and Instantaneous Frequency

Signal parameters

Center frequency fc (Hz): 50 Hz

Frequency deviation Δf (Hz): 10.0 Hz

Bit rate (bit/s): 4 bit/s

Coupled: Δf = h · Rb: Δf=4.0Hz

Modulation parameters

Amplitude A: 1.0

FSK type

Modulation index h: 1.00

Data and detection

Bit sequence

Detection type

SNR for simulation (dB): 15 dB

FSK modulated signal

Instantaneous frequency

Key Parameters and Formulas

The FSK signal is mathematically defined by several key parameters:

Carrier Frequency ( $f_n$ )

This is the center frequency around which the signal shifts. It is calculated as the arithmetic mean of the mark and space frequencies.

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

Frequency Deviation ( $\Delta f$ )

This parameter defines the maximum shift from the carrier frequency. It is calculated as half the difference between the mark and space frequencies.

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

Average Signal Power ( $P_{tot}$ )

Since the amplitude of the carrier wave ( $U_n$ ) remains constant, the total average power of the modulated signal is also constant and is given by:

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

FSK as a Form of Frequency Modulation (FM)

FSK can be considered a special case of digital . The key difference is the nature of the modulating signal: in analog FM, it is a continuous analog waveform (like audio), while in FSK, the modulating signal is a discrete, rectangular digital signal representing the binary data stream.

Simple FSK systems can introduce abrupt phase changes when switching between frequencies, which can cause spectral broadening. To mitigate this, more advanced schemes like Continuous Phase FSK (CPFSK) are used, ensuring a smooth phase transition between symbols. This improves spectral efficiency and leads to even more advanced techniques like MSK and GMSK.

Advantages, Disadvantages, and Applications

Advantages

Noise Immunity: Very good resistance to amplitude noise compared to ASK.
Simplicity: FSK modulators and demodulators are relatively simple and inexpensive to implement.
Constant Power: The constant amplitude envelope is suitable for use with power-efficient non-linear amplifiers.

Disadvantages

Bandwidth Inefficiency: Basic FSK is less spectrally efficient than PSK or QAM, requiring a wider frequency band for a given data rate.

Common Applications

Due to its robustness and simplicity, FSK is used in a variety of systems, especially where bandwidth is not the primary constraint:

Early telephone-line modems (e.g., Bell 103 standard at 300 bps).
Caller ID (DTMF and FSK are used for sending the caller's number).
Low-power radio systems and license-free bands.
Amateur radio, especially for data modes like RTTY (Radio Teletype).
Some RFID systems.