Frequency-shift keying

The frequency shift keying (English Frequency Shift Keying FSK) is a modulation technique and used for the transmission of digital signals, for example through a radio channel. It is related to the analog frequency modulation and is insensitive to how these disorders.

In the frequency shift, the carrier frequency of a periodic sinusoidal oscillation between a set of different frequencies will be changed, which represent the individual transmission symbols.

Properties

A transmission symbol is assigned in the modulation of a particular transmission frequency, in demodulating the detection of a particular frequency and the output of the corresponding symbol for further data processing. An essential parameter of the frequency shift is the integer number of the available transmission frequencies.

In the simplest case, there are only two different symbols before, this is referred to as binary FSK, and there are only two different symbol frequencies f1 and f2 are required. Only in this case the bit rate is equal to the symbol rate. If multiple frequencies are used, this is referred to as M- G, wherein M is the number of symbols or the different frequencies. For example, using 4 -FSK, four different transmitter frequencies and may be due to four transmit symbols transmitted per symbol two bits.

Other parameters are the FSK frequency deviation which indicates the amount of spacing between the frequency values ​​farthest is:

Alternatively, can be found in the literature which used different definitions which the frequency deviation as the distance from the carrier frequency fc defined using the following relationship:

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

The modulation index should be selected so that the two frequencies can be distinguished. This is the case, which is a decision interval of one symbol, continuous phase and binary FSK at ηopt ≈ 0.715 at the smallest possible negative correlation. Non- correlated the individual FSK frequencies are if they are orthogonal to each other. This is an integer and positive for the coherent demodulation in which the phase position of the carrier frequency is reconstructed in the receiver, with n, wherein

The case. The maximum symbol rate is calculated at n = 1 with two symbols per Hz bandwidth. In incoherent demodulation without support reconstruction in the recipient are at the FSK

Orthogonal. The maximum symbol rate is calculated at n = 1 then with one symbol per Hz bandwidth.

Modulator

Switching between the individual frequencies can be accomplished in several ways. The easiest way is to switch depending on the desired icon, between the different frequency generators. Since the individual frequency generators arbitrary phase angles from one another, carried on each changeover times usually a discontinuous transition in the waveform. This transition results in an undesirable high bandwidth requirement, and therefore, this form is also referred to as "hard FSK". An improvement of the modulator is that the switching takes place with a continuous phase profile as shown in the input image. This form is also known as CPFSK (English for Continuous Phase FSK).

Since the bandwidth is usually in limited supply, the switching is replaced by a continuous course. In the limiting case, the envelope is deformed to a Gaussian curve. This results in the smallest time - bandwidth requirements and it is called a "soft G ". By not abrupt switching of the transmission frequencies, however, there is also inter-symbol interference.

To improve the noise immunity in the demodulation, the single symbol frequencies can be chosen such that they are orthogonal to each other at a certain symbol rate. In this case, the intersymbol interference between the individual symbols is minimized. In binary FSK and a symbol duration of T, the two frequencies are then orthogonal to each other when the frequency deviation, filled with n integer and positive, the following condition:

Demodulator

The demodulator is used again to extract from the signal of the modulator, the original digital data sequence. Since the information is located only in the frequency, a signal processing is carried out usually prior to demodulation, comprising the steps of:

• Removal of the DC component including an ongoing readjustment of the zero point in the received signal.
• An amplitude limiting to always have one in about the same strong reception signal with an approximately constant amplitude at the demodulator input. This eliminates glitches and compensated differently strong received signals, which can be caused to a radio channel, for example, by fading.

For the subsequent demodulation several methods are available, which differ in the spectral efficiency, the circuit complexity and immunity. A distinction is made between coherent and non-coherent FSK demodulation.

Coherent FSK demodulator

In coherent demodulation or synchronous demodulation, the demodulator must have both the carrier frequency and the phase position of the transmitted signal to reconstruct. This is only possible if a continuous phase shift keying is used on the modulator side. The coherent demodulation caused Although a higher circuit complexity, but has the advantage that the potentially possible symbol rate, and thus directly proportional to the bit rate can be set higher than in the non-coherent demodulation. There is thus a higher spectral efficiency, measured in bits per hertz of bandwidth, before. In addition, the coherent FSK demodulation is less susceptible to interference.

Circuitry may be used for receiver-end reconstruction of the carrier frequency and the phase position of a voltage-controlled oscillator. In digitally implemented FSK demodulators numerically controlled oscillators are used. For controlling the oscillators in dependence on the received frequency, a phase -locked loop is necessary. Special adaptation of the phase locked loops for digital demodulation are known in the English-language specialist literature mostly under names such as Costas loop.

The frequencies obtained from the local oscillator are then multiplied with the received signal, as shown in the adjacent diagram for a binary FSK with the two local frequencies f1 and f2. Followed by an integration stage, which extends over the duration of a symbol. The output of each integrator is then evaluated by a decision stage and output the appropriate binary value for further data processing.

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

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

Alternatively, and equivalent to the above method, a coherent FSK demodulation can also be done by means of matched filter. Here, a matched filter is required for each of the symbol frequency, which has a transfer function of the respective transmit frequency for the duration of a symbol as an impulse response.

Non- coherent FSK demodulator

In the non-coherent demodulation of the expense of a phase- controlled oscillator and the circuit complexity is omitted reduced.

For implementing different methods can be used. In the adjacent circuit for a binary demodulator, the two frequencies f1 and f2 derived from a free-running oscillator and it is first, for each frequency of the complex baseband signal made ​​formed from the real and imaginary part. After integration and formation of the amount sent, binary value is determined by a decision stage.

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

And has with otherwise identical parameters is lower by a half symbol rate as the coherent demodulation.

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

• The use of band pass filters, each followed by envelope detectors. A comparator decides which filter provides the greatest amount value and returns the corresponding digital signal.
• As spectral methods such as fast Fourier transform can be used. With only a few transmission frequencies may be used with the reduced amount of calculation and the Goertzel algorithm. It should be noted, the block-based processing of such algorithms, which reduces the maximum symbol rate under certain circumstances.
• In the early days of digital signal processing also counter stages were used to determine the duration between two zero crossings of incoming signal. This method is associated with increased decision errors compared to the other methods.

Applications

Welcome response from a called fax.

FSK modulation method is widely used in telecommunications, both for data transmission lines, as well as in the radio. In the measurement and control technology, it is used for data transmission according to the HART protocol. Some brands of datasettes it was used for easy data recording.

The oldest application is the wireless telegraphy.

The musical is the acoustic response back, outputting a fax to call. The second and third signal contains data that / s were modulated in FSK on a 1750 Hz carrier according to the standard V.21 300 bits. Low corresponds to the frequency 1650 Hz, 1850 Hz correspond to high in the logarithmic Fourier representation in the adjacent figure these frequencies, the two adjacent peaks left in the spectrum.

Extensions of the frequency shift

GMSK and GFSK Gaussian Minimum Shift Keying and Gaussian Frequency Shift Keying FSK method are preceded by a Gaussian filter. Thus the steep flanks are flattened digital signals, resulting in that the high-frequency components of the signal disappear. Thus less bandwidth will be required for transmission of the signal.

GMSK is used, for example, the mobile phone standard Global System for Mobile Communications (GSM). In GSM, the bits of the signal as 3.7 microseconds wide rectangles to 18.5 microseconds long Gaussian pulses are. The resulting partially resulting overlays ( intersymbol interference ) and resulting misinterpretation of adjacent bits is balanced after demodulation by the error correction of the Viterbi algorithm.

AFSK A special form of frequency shift keying is the Audio Frequency Shift Keying ( FSK = Low Frequency ). Here, a low-frequency signal is frequency shift keyed in and subsequently modulated onto a radio frequency carrier.