Digital signal

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This article is about digital signals in electronics. For digital data and systems, see Digital data.
For a broader coverage related to this topic, see Signal (electrical engineering).

A digital signal is a physical signal that is a representation of a sequence of discrete values (a quantified discrete-time signal), for example of an arbitrary bit stream, or of a digitized (sampled and analog-to-digital converted) analog signal. The term digital signal can refer to either of the following:

  1. any continuous-time waveform signal used in digital communication, representing a bit stream or other sequence of discrete values
  2. a pulse train signal that switches between a discrete number of voltage levels or levels of light intensity, also known as a line coded signal or baseband transmission, for example a signal found in digital electronics or in serial communications, or a pulse code modulation (PCM) representation of a digitized analog signal.

A signal that is generated by means of a digital modulation method (digital passband transmission), to be transferred between modems, is in the first case considered as a digital signal, and in the second case as converted to an analog signal.

Digital signal

Discussion[edit]

Discrete cosine waveform with frequency of 50 Hz and a sampling rate of 1000 samples/sec, easily satisfying the sampling theorem for reconstruction of the original cosine function from samples.

A digital signal is a discrete-time signal for which not only the time but also the amplitude has been made discrete; in other words, its samples take on only values from a discrete set (a countable set that can be mapped one-to-one to a subset of integers). If that discrete set is finite, the discrete values can be represented with digital words of a finite width. Most commonly, these discrete values are represented as fixed-point words (either proportional to the waveform values or companded) or floating-point words.

After sampling, the process of converting a continuous-valued discrete-time signal to a digital (discrete-valued discrete-time) signal is known as analog-to-digital conversion. It usually proceeds by replacing each original sample value by an approximation selected from a given discrete set (for example by truncating or rounding), a process known as quantization. This process loses information, and so discrete-valued signals are only an approximation of the continuous-valued discrete-time signal, itself only an approximation of the original continuous-valued continuous-time signal.

Common practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 32-bit (4.3 billion levels), and so on, though any number of quantization levels is possible, not just powers of two.

Waveforms in digital systems[edit]

A digital 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 representing the two states of a Boolean value (0 and 1) is referred to as a digital signal, even though it is an analog voltage waveform, since it is interpreted in terms of only two levels.

The clock signal is a special digital signal that is used to synchronize 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 idealised 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 indeed may not correspond to either a logically high or low voltage.

Logic voltage levels[edit]

Hobbyist frequency counter circuit built almost entirely of TTL logic chips.
Main article: logic level

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 behaviour 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

See also[edit]