Frequency shift keying

Creation of a binary FSK signal.
Above: source data as a sequence of logical 1 and logical 0 .
Middle: Unmodulated carrier frequency
Below: Modulated FSK signal.

The frequency shift keying (English frequency shift keying , FSK) is a modulation technique and is used for transmission of digital signals , for example via a radio channel . It is related to analog frequency modulation and, like this, is insensitive to interference.

With frequency shift keying, the carrier frequency of a periodic sinusoidal oscillation is changed between a set of different frequencies that represent the individual transmission symbols.

properties

In the case of modulation, a transmission symbol is assigned to a specific transmission frequency; during demodulation, a specific frequency is recognized and the corresponding symbol is output for further data processing. An essential parameter of frequency shift keying is the integer number of available transmission frequencies.

In the simplest case there are only two different symbols, this is also referred to as binary FSK, and only two different symbol frequencies f ₁ and f _{2 are} required. Only in this case is the bit rate equal to the symbol rate. If multiple frequencies are used, this is calledM-FSK , where M stands for the number of symbols or the different frequencies. For example, 4-FSK uses four different transmission frequencies and can transmit two bits per symbol due to four transmission symbols.

Further parameters of the FSK are the frequency deviation , which indicates how much distance there is between the most distant frequency values :

${\displaystyle \Delta f=|f_{\mathrm {max} }-f_{\mathrm {min} }|\,}$.

Alternatively, the literature also contains definitions that deviate from this, which define the frequency deviation as the distance from the carrier frequency f _c with the following relationship:

${\displaystyle f_{c}={\frac {f_{\mathrm {min} }+f_{\mathrm {max} }}{2}},\qquad \Delta f'=f_{\mathrm {max} }-f_{c}=f_{c}-f_{\mathrm {min} }={\frac {\Delta f}{2}}}$

The modulation index η is the product of the stroke and the duration T of a symbol:

${\displaystyle \eta =2\cdot \Delta f'\cdot T\,}$

The modulation index should be chosen so that the two frequencies can be easily distinguished. This is the case with the smallest possible negative correlation , which is η _opt ≈ 0.715 for a decision interval of one symbol, continuous phase and binary FSK . The individual FSK frequencies are not correlated if they are orthogonal to one another. At n, this is an integer and positive for coherent demodulation, in which the phase position of the carrier frequency is reconstructed in the receiver

${\displaystyle \eta ={\frac {n}{2}},\qquad \Delta f'={\frac {n}{2\cdot T}}}$

the case. The maximum symbol rate results from n = 1 with two symbols per Hz bandwidth. In the case of incoherent demodulation without carrier reconstruction in the receiver, the FSK are there to help

${\displaystyle \eta =n,\qquad \Delta f'={\frac {n}{T}}}$

orthogonal to each other. The maximum symbol rate then results with n = 1 with one symbol per Hz bandwidth.

modulator

Switching between the individual frequencies can be done in different ways. The simplest possibility is to switch between the different frequency generators depending on the desired symbol. Since the individual frequency generators have any phase relationship to one another, there is generally a discontinuous transition in the signal curve at the individual switching times . This transition leads to an undesirably high bandwidth requirement , which is why this form is also referred to as “hard FSK”. One improvement of the modulator is that the switching takes place with a continuous phase curve, as shown in the input figure. This form is also calledCPFSK (English for Continuous Phase FSK ) called.

Since the bandwidth is usually limited, the switching is replaced by a continuous process. In the borderline case, the envelope is deformed up to a Gaussian curve ( GFSK ). This results in the smallest time bandwidth requirement and one speaks of a "soft FSK". However, the non-abrupt switching of the transmission frequencies also leads to intersymbol interference .

In order to improve the immunity to interference during demodulation, the individual symbol frequencies can be selected in such a way that they are orthogonal to one another at a certain symbol rate . In this case, the intersymbol interference between individual symbols becomes minimal. With binary FSK and a symbol duration of T , the two frequencies are orthogonal to each other if the frequency deviation, with n being an integer and positive, fulfills the following condition:

${\displaystyle \Delta f'={\frac {1}{T}}\cdot {\frac {n}{2}},\qquad n\in \lbrace 1,2,3,\ldots \rbrace }$

Demodulator

The demodulator is used to recover the original digital data sequence from the signal from the modulator. Since the information is only contained in the frequency, signal processing is usually carried out before demodulation, which includes the following steps:

• Removal of the direct component in the received signal including an ongoing readjustment of the zero point.
• An amplitude limitation in order to always have an approximately equally strong received signal with an approximately constant amplitude at the demodulator input. This eliminates interference pulses and compensates for received signals of different strengths, which can be caused by fading on a radio channel, for example .

There are several methods available for the subsequent demodulation, which differ in terms of spectral efficiency , circuit complexity and interference immunity. A basic distinction is made between coherent and non-coherent FSK demodulation.

Coherent FSK demodulator

Coherent FSK demodulator (phase locked loop not shown)

With coherent demodulation, or also synchronous demodulation, the demodulator must reconstruct both the carrier frequency and the phase position of the transmission signal. This is only possible if a constant phase change is used on the modulator side. The coherent demodulation requires a higher circuitry complexity, but has the advantage that the potentially possible symbol rate, and thus the bit rate, can be selected to be higher than in the case of non-coherent demodulation. There is thus a higher spectral efficiency, measured in bits per Hertz bandwidth. In addition, the coherent FSK demodulation is less sensitive to interference.

In terms of circuitry, a voltage-controlled oscillator can be used to reconstruct the carrier frequency and its phase position at the receiver end. Numerically controlled oscillators are used in digitally implemented FSK demodulators . A phase-locked loop is required to control the oscillators as a function of the receiving frequencies . Special adaptations of phase-locked loops for digital demodulation are known in the mostly English-language specialist literature under names such as Costas Loop .

The frequencies obtained from the local oscillator are then multiplied by the received signal, as shown in the adjacent figure for a binary FSK with the two local frequencies f ₁ and f ₂ . This is followed by an integration stage that extends over the duration of a symbol. The output of the individual integrators is then evaluated by a decision-making stage and the appropriate binary value is output for further data processing.

The maximum achievable bit rate bps , which is equal to the symbol rate for binary FSK, depends only on the frequency deviation and is:

${\displaystyle bps=2\cdot \Delta f}$

The special case with a modulation index equal to 0.5 is also called minimum shift keying (MSK). A special feature is that this process is identical to the digital modulation process Quadrature Phase Shift Keying (QPSK) with a phase offset of π / 2 and half-wave pulse shaping.

As an alternative, and equivalent to the above method, coherent FSK demodulation can also take place using a matched filter . A matched filter is required for each symbol frequency, which has the transmission function of the respective transmission frequency as an impulse response for the duration of a symbol .

Non-coherent FSK demodulator

Non-coherent FSK demodulator

With non-coherent demodulation, there is no need for a phase-controlled oscillator and the circuit complexity is reduced.

Different methods can be used to implement this. In the adjacent circuit for a binary demodulator, the two frequencies f ₁ and f _{2 come} from a free-running oscillator and the complex baseband signal consisting of real and imaginary components is initially formed for each frequency. After integration and formation of the amount, the binary value sent is determined via a decision-making level.

The maximum achievable bit rate for binary FSK with non-coherent demodulation is:

${\displaystyle bps=\Delta f}$

and has a symbol rate that is half lower than the coherent demodulation with otherwise the same parameters.

In addition, there are other non-coherent FSK demodulation methods such as:

• Use of band-pass filters with subsequent envelope detectors . A comparator decides which filter delivers the largest absolute value and outputs the associated digital signal.
• Spectral methods such as the fast Fourier transformation can be used. With only a few transmission frequencies, the Goertzel algorithm can also be used with reduced computational effort . Note the block-oriented processing of these algorithms, which may reduce the maximum symbol rate.
• In the early days of digital signal processing, counter stages were also used to determine the duration between two zero crossings of the received signal. This method is afflicted with more decision-making errors than the other methods.

Applications

Fourier representation of the DIS signal of a fax

Welcome reply from a called fax ^{? / i}

The FSK modulation method is used in a variety of ways in telecommunications , both for data transmission over lines and in radio. It is used in measurement and control technology for data transmission according to the HART protocol. With some makes of Datasette it was used for simple data recording.

The oldest application is wireless telegraphy .

The sound sample reproduces the acoustic answer that a fax gives to a call. The second and third signals contain data that have been modulated onto a 1750 Hz carrier at 300 bit / s in FSK according to the V.21 standard. Low corresponds to the frequency 1650 Hz, High 1850 Hz. In the logarithmic Fourier representation in the adjacent figure, these frequencies correspond to the two neighboring peaks on the left in the spectrum.

The English piccolo system used 32 tones (Mark D piccolo) and later 6 tones (Mark F piccolo).

Frequency shift keying extensions

GMSK and GFSK
Gaussian Minimum Shift Keying and Gaussian Frequency Shift Keying are FSK methods with an upstream Gaussian filter . This flattens the steep edges of digital signals, which means that the high-frequency components of the signal are omitted. This means that less bandwidth is required to transmit the signal.

GMSK is used, for example, in the Global System for Mobile Communications (GSM) wireless standard . With GSM, the bits of the signal change from 3.7 µs wide rectangles to 18.5 µs long Gaussian pulses. The resulting overlapping ( intersymbol interference ) and the resulting misinterpretation of neighboring bits is compensated for after demodulation by the error correction of the Viterbi algorithm .

AFSK
A special form of frequency shift keying is audio frequency shift keying (= low frequency frequency shift keying ). Here, a is the low-frequency signal keyed in frequency and then subsequently to a high-frequency - carrier modulated. This means that the AFSK modulates twice.

literature

• Karl-Dirk Kammeyer : message transmission . 4th revised and supplemented edition. Vieweg + Teubner, Wiesbaden 2008, ISBN 978-3-8351-0179-1 .
• Rudolf Mäusl, Jürgen Göbel: Analog and digital modulation methods. Baseband and carrier modulation . Hüthig, Heidelberg 2002, ISBN 3-7785-2886-6 .

Individual evidence

1. ^ John B. Anderson: Digital Transmission Engineering . 2nd Edition. Wiley Interscience, 2005, ISBN 0-471-69464-9 , pp. 126 to 127 .
2. ↑ Ross Bradshaw: `` Diplomatic Wireless Service, Part 3. '' In: `` [[Practical Wireless]] '', June 2012, page 64.