Digital signal

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The term digital signal is used to refer to more than one concept. It can refer to discrete-time signals that have a discrete number of levels, for example a sampled and quantified analog signal, or to the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a digital modulation method which is considered as converted to an analog signal, while it is considered as a digital signal in the second case.

Discrete-time signals

Discrete sampled signal

Digital signal

An analog signal is a datum that changes over time—say, the temperature at a given location; the depth of a certain point in a pond; or the amplitude of the voltage at some node in a circuit—that can be represented as a mathematical function, with time as the free variable (abscissa) and the signal itself as the dependent variable (ordinate). A discrete-time signal is a sampled version of an analog signal: the value of the datum is noted at fixed intervals (for example, every microsecond) rather than continuously.

If individual time values of the discrete-time signal, instead of being measured precisely (which would require an infinite number of digits), are approximated to a certain precision—which, therefore, only requires a specific number of digits—then the resultant data stream is termed a digital signal. The process of approximating the precise value within a fixed number of digits, or bits, is called quantization.

In conceptual summary, a digital signal is a quantized discrete-time signal; a discrete-time signal is a sampled analog signal.

In the Digital Revolution, the usage of digital signals has increased significantly. Many modern media devices, especially the ones that connect with computers use digital signals to represent signals that were traditionally represented as continuous-time signals; cell phones, music and video players, personal video recorders, and digital cameras are examples.

In most applications, digital signals are represented as binary numbers, so their precision of quantization is measured in bits. Suppose, for example, that we wish to measure a signal to two significant decimal digits. Since seven bits, or binary digits, can record 128 discrete values (viz., from 0 to 127), those seven bits are more than sufficient to express a range of one hundred values.

Waveforms in digital systems

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

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 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.

See also

• Digital signal processing
• Nyquist–Shannon sampling theorem
• Whittaker–Shannon interpolation formula
• Intersymbol interference in digital communication