## Amplitude-shift keying

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Amplitude-shift keying ASK is a form of amplitude modulation that represents digital data as variations in the amplitude of a carrier wave. In an ASK system, the binary symbol 1 is represented by transmitting a fixed-amplitude carrier wave and fixed frequency for a bit duration of T seconds. If the signal value is 1 then the carrier signal will be transmitted; otherwise, a signal value of 0 will be transmitted. Any digital modulation scheme uses a finite number of distinct signals to represent digital data.

ASK uses a finite number of amplitudes, each assigned a unique pattern of binary digits. Usually, each amplitude encodes an equal number of bits. Each pattern of amplitude shift keying binary signal space diagram forms the symbol that is represented by the particular amplitude. The demodulatorwhich is designed specifically for the symbol-set used by the modulator, determines the amplitude of the received signal and maps it back to the symbol it represents, thus recovering the original data.

Frequency and phase of the carrier are kept constant. Both ASK modulation and demodulation processes are relatively inexpensive.

The ASK technique amplitude shift keying binary signal space diagram also commonly used to transmit digital data over optical fiber. For LED transmitters, binary 1 is represented by a short pulse of light and binary 0 by the absence of light. Laser transmitters normally have a fixed "bias" current that causes the device to emit a low light level. This low level represents binary 0, while a higher-amplitude lightwave represents binary 1. The simplest and most common form of ASK operates as a switch, using the presence of a carrier wave to indicate a binary one and its absence to indicate a binary zero.

This type of modulation is called on-off keying OOKand is used at radio frequencies to transmit Morse code referred to as continuous wave operation. More sophisticated encoding schemes have been developed which represent data in groups using additional amplitude levels. For instance, a four-level encoding scheme can represent two bits with each shift in amplitude; an eight-level scheme can represent three bits; and so on.

These forms of amplitude-shift keying require a high signal-to-noise ratio for their recovery, as by their nature much of the signal is transmitted at reduced power. ASK system can be divided into three blocks. The first one represents the transmitter, the second one is a linear model of the effects of the channel, the third one shows the structure of **amplitude shift keying binary signal space diagram** receiver.

The following notation is used:. Different symbols are represented with different voltages. Considering the picture, the symbols v[n] are generated randomly by the source S, then the impulse generator creates impulses with an area of v[n].

These impulses are sent to the filter ht to be sent through the channel. In other words, for each symbol a different carrier wave is sent with the relative amplitude.

In this relationship, the second term represents the symbol to be extracted. The others are unwanted: If the filters are chosen so that g t will satisfy the Nyquist ISI criterion, then there will be no intersymbol interference and the value of the sum will be zero, so:.

The probability density function of having an error of a given size can be modelled by a Gaussian function; the mean value will be the relative sent value, and its variance will be given by:. The probability of making an error after a single symbol has been sent is the area of the Gaussian function falling under the functions for the other symbols. It is shown in cyan for just one of them. The total probability of making an error can be expressed in the form:. In order to do that, we can move the origin of the reference wherever we want: We are in a amplitude shift keying binary signal space diagram like the one shown in the following picture:.

The value we are looking for will be given by the following integral:. Putting all these results together, amplitude shift keying binary signal space diagram probability to make an error is:. This relationship is valid when there is no intersymbol amplitude shift keying binary signal space diagram, i.

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