# Digital signal

A binary signal, also known as a logic signal, is a digital signal with two distinguishable levels

A digital signal is a signal that represents a sequence of discrete values.[1][2] A logic signal is a digital signal with only two possible values,[3][4] and describes an arbitrary bit stream. Other types of digital signals can represent three-valued logic or higher valued logics.

A digital signal is a physical quantity that is alternating between a discrete set of waveforms.[5] Alternatively, a digital signal may be considered to be the sequence of codes represented by such a physical quantity.[6] The physical quantity may be the alternating current or voltage of an electrical signal, the light intensity of an optical signal, the signal strength of a radio signal or acoustic signal, the magnetization of a magnetic storage media, et cetera. Digital signals are present in all digital electronics, notably computing equipment and data transmission.

A received digital signal may be impaired by noise and distortions without necessarily affecting the digits

With digital signals, system noise, provided it is not too great, will not change the quantification whereas with signals handled using analog processing, noise always degrades the operation to some degree.

## Definitions in different contexts

The term digital signal has related definitions in different contexts:

### In digital electronics

A five level PAM digital signal

In digital electronics a digital signal is a pulse train (a pulse amplitude modulated signal), i.e. a sequence of fixed-width square-wave electrical pulses or light pulses, each occupying one of a discrete number of levels of amplitude.[7][8] A special case is a logic signal or a binary signal, which varies between a low and a high signal level.

### In signal processing

In signal processing, a digital signal is an abstraction that is discrete in time and amplitude, meaning it only exists at certain time instants.

In digital signal processing, a digital signal is a representation of a physical signal that is a sampled and quantified. A digital signal is an abstraction which is discrete in time and amplitude. The signal's value only exists at regular time intervals, since only the values of the corresponding physical signal at those sampled moments are significant for further digital processing. The digital signal is a sequence of codes drawn from a finite set of values.[6] The digital signal may be stored, processed or transmitted physically as a pulse code modulation (PCM) signal.

### In communications

An AMI coded digital signal used in baseband transmission (line coding)
A frequency shift keying (FSK) signal is alternating between two waveforms, and allows passband transmission. It is considered digital in literature on data transmission.

In digital communications, a digital signal is a continuous-time physical signal, alternating between a discrete number of waveforms,[5] representing a bit stream message. The shape of the waveform depends the transmission scheme, which may be either:

1. a line coding scheme, which produces a pulse-modulated signal, allowing baseband transmission; or
2. a digital modulation scheme, allowing passband transmission over long wires or over a limited radio frequency band. Such a carrier-modulated sine wave is considered a digital signal in literature on digital communications and data transmission,[9] but considered as a bit-stream converted to an analog signal in electronics and computer networking.[10]

## Logic signal

A logic signal waveform: (1) low level, (2) high level, (3) rising edge, and (4) falling edge.

In computer architecture and other digital systems, a waveform that switches between two voltage levels (or less commonly, other waveforms) representing the two states of a Boolean value (0 and 1, or Low and High, or false and true) is referred to as a digital signal or logic signal or binary signal when it is interpreted in terms of only two possible digits.

The clock signal is a special digital signal that is used to synchronize many (but not all) digital circuits. The image shown can be considered the waveform of a clock signal. Logic changes are triggered either by the rising edge or the falling edge.

The given diagram is an example of the practical pulse and therefore we have introduced two new terms that are:

• Rising edge: the transition from a low voltage (level 1 in the diagram) to a high voltage (level 2).
• Falling edge: the transition from a high voltage to a low one.

Although in a highly simplified and idealized model of a digital circuit we may wish for these transitions to occur instantaneously, no real world circuit is purely resistive and therefore no circuit can instantly change voltage levels. This means that during a short, finite transition time the output may not properly reflect the input, and will not correspond to either a logically high or low voltage.

## Logic voltage levels

File:Hobby frequency counter.jpg
Hobbyist frequency counter circuit built almost entirely of TTL logic chips.

The two states of a wire are usually represented by some measurement of an electrical property: Voltage is the most common, but current is used in some logic families. A threshold is designed for each logic family. When below that threshold, the wire is "low", when above "high." Digital circuits establish a "no man's area" or "exclusion zone" that is wider than the tolerances of the components. The circuits avoid that area, in order to avoid indeterminate results. It is usual to allow some tolerance in the voltage levels used; for example, 0 to 2 volts might represent logic 0, and 3 to 5 volts logic 1. A voltage of 2 to 3 volts would be invalid, and occur only in a fault condition or during a logic level transition. However, few logic circuits can detect such a condition and most devices will interpret the signal simply as high or low in an undefined or device-specific manner. Some logic devices incorporate schmitt trigger inputs whose behavior is much better defined in the threshold region, and have increased resilience to small variations in the input voltage.

The levels represent the binary integers or logic levels of 0 and 1. In active-high logic, "low" represents binary 0 and "high" represents binary 1. Active-low logic uses the reverse representation.

Examples of binary logic levels:
Technology L voltage H voltage Notes
CMOS 0 V to VDD/2 VDD/2 to VDD VDD = supply voltage
TTL 0 V to 0.8 V 2 V to VCC VCC is 4.75 V to 5.25 V
ECL -1.175 V to VEE 0.75 V to 0 V VEE is about -5.2 V. VCC=Ground

## Modulation

To create a digital signal, an analog signal must be modulated with a control signal to produce it. As we have already seen, the simplest modulation, a type of unipolar line coding is simply to switch on and off a DC signal, so that high voltages are a '1' and low voltages are '0'.

In digital radio schemes one or more carrier waves are amplitude or frequency or phase modulated with a signal to produce a digital signal suitable for transmission.

In Asymmetric Digital Subscriber Line over telephone wires, ADSL does not primarily use binary logic; the digital signals for individual carriers are modulated with different valued logics, depending on the Shannon capacity of the individual channel.

## Clocking

File:FF Tsetup Thold Toutput.svg
Clocking digital signals through a clocked flip-flop

Often digital signals are "sampled" by a clock signal at regular intervals by passing the signal through an "edge sensitive" flip-flop. When this is done the input is measured at those points in time, and the signal from that time is passed through to the output and the output is then held steady till the next clock.

This process is the basis of synchronous logic, and the system is also used in digital signal processing.

However, asynchronous logic also exists, which uses no single clock, and generally operates more quickly, and may use less power, but is significantly harder to design.

## References

1. Digital Design with CPLD Applications and VHDL By Robert K. Dueck: "A digital representation can have only specific discrete values"
2. Proakis, John G.; Manolakis, Dimitris G. (2007-01-01). Digital Signal Processing. Pearson Prentice Hall. ISBN 9780131873742.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
3. [1]
4. Art of Electronics, Horowitz and Hill.
5. Analogue and Digital Communication Techniques: "A digital signal is a complex waveform and can be defined as a discrete waveform having a finite set of levels"
6. Vinod Kumar Khanna, Digital Signal Processing, 2009: A digital signal is a special form of discrete-time signal which is discrete in both time and amplitude, obtained by permitting each value (sample) of a discrete-time signal to acquire a finite set of values (quantization), assigning it a numerical symbol according to a code ... A digital signal is a sequence or list of numbers drawn from a finite set.
7. B. SOMANATHAN NAIR, Digital electronics and logic design 2002: "Digital signals are fixed-width pulses, which occupy only one of two levels of amplitude."
8. Joseph Migga Kizza, Computer Network Security 2005
9. J.S.Chitode, Communication Systems, 2008: "When a digital signal is transmitted over a long distance, it needs CW modulation."
10. Fred Halsall, Computer Networking and the Internet: "In order to transmit a digital signal over an analog subscriber line, modulated transmission must be used; thas is the electrical signal that represents the binary bit stream of the source (digital) output must first be converted to an analog signal that is compatible with a (telephony) speech signal."