Digitalsignal

A digital signal (from the Latin digitus = finger, fingers counting ) is a special form of a signal that has a defined and stepped value stock and also defined in the time sequence only at certain periodic times on the one hand or has a change in signal value. It may consist of an analog signal, which describes the time profile of a continuous physical quantity, be formed by the quantization and sampling which is performed at defined time points. The digital values ​​are usually encoded as binary numbers, so that its quantization is given in bits.

Digital signals play an important role in communications technology and digital signal processing. Examples of digital signals such as video signals that are transmitted when DVI and HDMI standard or the audio signals in Dolby Digital and S / PDIF. Also, the data transfer via DSL, wireless and mobile communications standards GSM and UMTS is also based on digital signals as modern computer technology.

• 3.1 Transfer
• 3.2 Transfer and interference
• 3.3 Differentiation from other value-discrete signals

General

The implementation of an analog signal into a digital signal in two steps which can be performed in any order:

• The sampling to convert a continuous-time signal into a discrete-time signal.
• The quantization, in order to convert a continuous-value signal into a discrete-value signal.

Depending on the application, different concept definitions common. The exact distinction between what is meant by a digital signal is usually obtained from the respective context: In signal theory as a mathematical representation used consequences which are clearly characterized by an " infinitely thin " pulse train in the time sequence. In contrast, in digital circuits, which are common in the field of digital technology, is a mathematical sequence by physical parameters such as an electrical voltage can not be displayed: The digital signal is in this case formed by a continuous-time course, with the continuous course changes only at certain times and between times the value is constant.

The sampling and education of the digital signal is usually carried out at constant time intervals, although this is not absolutely necessary.

Signal Theory

A digital signal x [ n] can be seen as a sequence of numbers, which come from a defined value stocks, are described. The index n is the time variable normalized to the sampling rate - usually takes place at constant sampling intervals Ts, the reciprocal is referred to as sampling rate or sampling frequency fs. In the adjacent figure, the exemplary course of an analog signal in gray and the resulting digital signal sequence formed in red with the following values:

Shown. It is essential that the values ​​between the sampling points is not zero, or may comprise other values, but are not defined. The illustration on integers are arbitrary.

The Nyquist-Shannon sampling theorem, in this case describes the effect that, in the sequence x [n] only the complete information of the analog waveform may be present, when the highest -frequency components are smaller than half the sampling frequency fa fs:

Digital technology

In digital technology, a digital signal is additionally formed with a sample-and - hold circuit 0th order and then presents a continuous-time course, which varies in its value only to the individual sampling times.

The individual time-discrete samples of the sequence are convolved with the rectangular function. The result is a digital signal, as exemplified in red in the figure beside. This profile f (t) can, at least approximately, for example, a voltage waveform can be physically realized in a digital circuit, and integrated circuits.

It should be noted that the convolution with the rectangular function in the conversion to the original analog waveform using a digital -to-analog converter (DAC), a distortion of the frequency spectrum occurs, which must be compensated by a corresponding filter. The distortion corresponding to the sinc function, which is the Fourier transform of the square function.

Example

When recording an audio CD each channel ( left / right) is the source signal is sampled 44,100 times per second. The sampling frequency is 44.1 kHz in this case. Higher-frequency details of the recorded source signal as half the sampling rate, in this case about 22 kHz are not recognized and removed when shooting by anti- aliasing filter.

The thus obtained individual samples ( " Samples" ) are still in their size continuously, that is, they can have any value. In order to display these values ​​in numerical form, they first need to quantization, a form of rounding, are fitted into a fixed - grid values ​​. Finer changes between the values ​​grid levels are not controlled or produce a change to a full stage. This word width, resolution is therefore chosen as finely as possible and at the audio CD includes 65,536 possible values ​​with a linear characteristic, that is, independent of signal size a constant resolution is used in the value range. The individual words per sample are shown in the audio CD by the encoding as binary numbers with 16 bits per word, the number of digits per word is also referred to as dynamic, and are then available for further processing, such as the recording on the disk to available.

Application

Transmission

Can only be transmitted signals that are continuous in time. Furthermore, even disorders such as thermal noise and other inaccuracies are added in components that exactly rule it out practically ( represented by voltage, field strength, etc.) to transfer a determine value. This means that each digital signal may be transmitted only in the form of an analog signal and must be then digitized at the receiver side.

In the simplest case, one simply assigns to each possible value of the digital signal to a value or range of values ​​of a physical quantity, which you transfer. In TTL technique, for example, the binary number "0" shown ... 0.4 (with positive logic) with a voltage of 0 V, and the "1" by 2.4 ... 5.0V.

Such an analog signal, a sudden, rapid changes in the course of which (such as the above described digital signal, the circuit design ), the undesirable characteristic of possessing a very wide range. This leads to interference in adjacent channels or channels must be used with a large bandwidth. Therefore, in today's digital transmission method of the digital signal with a continuous folded basic pulse with specific properties, such as the raised cosine filter. The result is also an analog signal.

Transmission and interference

A digital signal is less prone to interference in the transmission, as the signal level with a certain tolerance can still be assigned to the correct value. Each signal is always superimposed or disturbed by noise in the transmission. If the noisy signal digitized again, these effects will disappear by the quantization again. As long as the perturbations are not too large, one obtains the original signal again.

Therefore, digital signals are more suitable, as analog signals to be transmitted over long distances. If, ready to process the signal along the way repeater, ie digitize (possibly correct errors ) and then further end ( again analogous ), then removed it every time the unwanted noise and continues to send only the useful signal. Although a purely analog signal can be amplified also repeatedly, but you will also strengthened each time the noise with.

This makes it possible to transmit digital signals without loss and digitally transmitted or stored signals as often - and without sacrificing quality - to copy again.

At the end of the information processing chain, a conversion to an analog signal is to notify the people in the rule again required, eg from the audio CD into electrical voltage and sound pressure.

Demarcation from other value-discrete signals

A digital signal has to be both time - and value- discrete. In terms of circuit technology, the property of the time discreteness is also satisfied when the signal can change only at discrete points in time, but in between (time ) is constant and, as a continuously available. In addition, there also a number of value-discrete signals, which are no digital signals, however.

For example, which is a pulse width modulated signal is composed of a square wave of fixed frequency with variable duty cycle continuously. Also, a sequence of rectangular pulses, such as produced when measuring the rotational speed with a light barrier, not a digital signal. Although this signal is discrete values ​​, even in binary, but may change its value without being tied to a clock having the frequency of the pulses. Another example although colloquially common, but incorrect use of the term is the term " digital amplifier " for class - D amplifiers, which operate by means of pulse width modulation.

Importance

Due to the so-called digital revolution, the use of digital signals has dramatically increased. By now, most household appliances are based on either completely or at least in large part to digital signals. Communication systems such as the Internet and the mobile telephony network based on a digital signal. The advantages over analog technology are more versatile editing options and error-free storage capacity for a long time, for example, on CD- ROMs.